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ALAjV E. SHAPIRO

LIGHT, PRESSURE, AND RECTILINEAR PROPAGATION: DESCARTES

CELESTIAL OPTICS AND NEWTONS HYDROSTATICS

NEWTONS early encounter with the Cartesian scientific corpus-La Dioptrique, La Glomtbie and Principia philosophiae--left a permanent mark on his later scientific development. If Newtons contemporaries interpreted his work largely as a rejection of the Cartesian system of philosophy, today we understand the Cartesian influence to have been so pervasive and complex that Newton could not overcome it simply by refuting it. We still recognize the ultimate rejection of the Cartesian system, but we also see the many Cartesian concepts which Newton accepted, further developed, and finally incorporated into his own work.

Broadly speaking, we can characterize the Cartesian influence in the following way. While still an undergraduate Newton read Descartes scientific works and took from them primarily specific scientific concepts and techniques. We can, for example, see this in his optics, by his treatment of refraction from La Dioptrique; in his mathematics, by his researches in algebra, analytic geometry and calculus from La Geomt?trie; and in his mechanics, by his formulation of the law of inertia and calculation

This paper was originally part of my doctoral dissertation, Rays and Waves: A Study in Seventeenth- Century Optics (Yale University, 1970). I wish to thank Martin Klein, my dissertation adviser, who patiently offered me thoughtful and valuable advice; and David C. Lindberg, Clifford Truesdell, and Derek T. Whiteside, who read the dissertation and provided useful criticism and suggestions. Needless to say, I remain responsible for all errors.

t La Dioptrique, Les M&ores and La Gt!onv!Trie were published together with the Discours de la m&ode (Leyden, I 637). Descartes Principia philosophiae (Amsterdam, 1644) and the authorized French translation, Les Principes de la philosophie (Paris, 1647), will be cited as the Principles to avoid confusion with Newtons Philosophiae naturalis principia mathematics (London, 1687) which I will refer to as the Principia. My references will be to Oeuvres de Descartes, Charles Adam and Paul Tannery (eds.), II ~01s. + supplement (Paris, 18g7--1913) ; henceforth cited as AT. Since Newton read the Latin edition of the Principles, all my translations will be from the Latin; but I will include clarifying remarks added in the French translation, which I will give in square brackets. My references to the Principles will be by part and article, followed by a reference to both the Latin (AT, VIII, i) and French versions (AT, IX, ii).

Stud. Hist. Phil. Sci. 5 (1g74), no. 3 Printed in Great Britain.

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240 Studies in History and Philosojhy of Science

of centrifugal forces from the Principles.2 While Newton developed many of these specific Cartesian contributions, he rejected the core of the Cartesian natural philosophy, such as Descartes concepts of space and motion.

Newtons major objection to a continuum theory of light3 was that it violates the law of rectilinear propagation, since any pressure propagated in a fluid would diverge into the geometric shadow after passing through an aperture placed in its path. We meet this objection in one form or another almost wherever we turn: in his letters of 1672 to Ignace Gaston Pardies and Robert Hooke defending his theory of colour; in his second paper on light and colour in 1675 ; in all the editions of the Opticks save the first; and, where it might least be expected, in the Principia. Since these writings span a period of over half a century, we can surely say this was a firmly held conviction. To my knowledge, though, no one has ever attempted to explain the significance of the almost compulsive appearance and reappearance of this argument against continuum theories of light.

I will attempt to show that these objections represent a Cartesian influence, but not at all in the usually accepted sense: a straightforward rejection of the Cartesian theory of light as a pressure. Descartes explanation of light as the con&s or endeavour of the aetherial particles to recede from the centre of their vortex is often mistakenly referred to as a centrifugal pressure, but Descartes concept of conatm-the central concept of his theory of light-cannot be identified with pressure. Descartes denied the proper concept of pressure, which demands that at any point within a fluid the pressure acts equally in all directions; Descartes in fact denied that there were any pressures at all within a fluid. Moreover, he held that con&us acts in straight lines, thus making it ideal for explaining the rectilinear propagation of light. To assimilate

Alexandre Koyre, in his paper Newton and Descartes (jVerotonian Studies [Chicago: University of Chicago Press, 19681, 53-r14), presents a broad discussion of their relation. For optics, see A. I. Sabra, Theories of Light: From Descartes to .Newton (London: Oldbourne, rg67), 30-2; for mathematics, Derek T. White&de, Isaac Newton: Birth of a Mathematician, NoIvotes and Records of the Royul Sotie@ of London, rg (Ig64), 53-62; for mechanics, John Herivel, nhe Background to JVewtons Priruipia: A Study of Newtons Dynamical Researches in the Years 1664-84 (Oxford: Oxford University Press, tg65), 42-53, henceforth cited as Background; and Alan Gabbey, Force and Inertia in Seventeenth-Century Dynamics, Studies in History and Philosophy of Science, 2 (rg7*), I-68.

I will not use the expression wave theory of light to describe any seventeenth-century theory of light. Rather, I will use the expression continuum theory of light, and instead of the term corpuscular theory of light I will use the expression emission theory of light. These two types of theory are defined simply: in an emission theory of light there is a transport of matter from the luminous source to the eye; whereas in a continuum theory there is only a propagation of a state, such as a pressure or motion, through an intervening medium. I believe that the more common terminology when applied to seventeenth-century theories of light is misleading and admits too many contradictions.

Light, Pressure, and Rectilinear Propagation 241

Newtons criticism of Descartes theory of light to our interpretation of it and to identify conatus with pressure makes Descartes theory seem trivially ill-conceived and wrenches it out of its proper conceptual frame. Descartes built his theory of light primarily on his concept of conatus, and only secondarily on his model of the fluid through which the conatus, or light rays, are propagated. Fluid mechanics and optics were not yet related. If we fail to recognize this, we fail to recognize Newtons achievement in developing the concept of hydrostatic pressure and in placing the continuum theories of light in an entirely new context, that of fluid mechanics. The conceptual relation of hydrostatics and optics was so radically different for Descartes and Newton, that on the one occasion when Descartes did relate his hydrostatics to his theory of light, it tended to support his optics rather than to contradict it: while Descartes denied a proper concept of pressure, he did admit the weight of a fluid which acts in a unique direction, namely, in straight lines downwards. What has misled historians is that Descartes concept of conatus does lead to a proper concept of pressure, although Descartes himself could not take this step because of his commitments to the rectilinear propagation of light and traditional hydrostatics. Newton did take this step, and herein lies the origin of his hydrostatics and his objections to a continuum theory of light, namely, that a pressure propagated in a fluid violates the law of rectilinear propagation. Newtons argument cannot be viewed, as it commonly is, as a straightforward refutation of Descartes theory of light. Rather, Newtons objection should be viewed as a significant advance beyond Descartes ; it represents Newtons transformation of Descartes concept of conatus into a proper concept of hydrostatic pressure.

Even more significant than Newtons refutation of Descartes theory of light was his attempt to formulate a proper theoretical treatment of hydrostatics and, later, a theory of wave propagation in elastic media based on his newly-wrought concept of hydrostatic pressure. Newtons hydrostatics has been virtually ignored by historians of science. In part this is not unexpected, for this work was far less dramatic than his other scientific work and had but slight bearing on his broader world view. Moreover, Newtons treatment of hydrostatics is so compressed into a few terse pages of the Principia, that the precise nature of his approach is obscure. Even that terse treatment, though, has shown that his views on hydrostatics were relatively advanced for his time. The publication of Newtons early manuscript on hydrostatics, De gravitatione et aequipondio

jluidorum (c. 1668) which has not yet been analysed for its hydrostatical

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contents, will allow me to place Newtons achievement in hydrostatics in an entirely new light4 From an analysis of De grauitatione, it is apparent that Newtons insight into the fundamentals of hydrostatics was consider- ably in advance of his contemporaries and was not to be surpassed until the second quarter of the eighteenth century. This analysis will also allow me to establish that Newton had formulated the foundations of his hydrostatics by 1672 at the time of the publication of his first paper on his theory of light and colours. Newtons deep immersion in the Cartesian scientific corpus, his formulation of hydrostatics, and the development of his own theory of light and colours, thus all occurred in precisely the same period of time, and I will demonstrate how these endeavours converged in his attack on the continuum theories of light.

In his correspondence Descartes repeatedly insists that his theory of light can be understood only within the context of his entire physics and, in particular, with its relation to the subtle matter or aether. Yet Descartes says virtually nothing about the aether in La Dioptrique, other than to postulate its existence. We can therefore readily appreciate his caveat lector in the first discourse of La Dioptrique, where he tells us that this work is primarily meant for artisans so that they can improve the telescope. Since all they need know about light is how it is refracted and enters the eye, I need not undertake to explain its true nature. And I believe that it will suffice that I make two or three comparisons that help to conceive it . . ..6 Hence, relying unduly on La Dioptrique for Descartes theory of light can yield an extremely misleading account of his theory. Following Descartes advice, I believe that we must turn to his Principia philosophiae rather than to La Dioptrique for an understanding of his theory of light. Only in approaching the matter in this way, which has not yet been done thoroughly, will we be able to appreciate Descartes theory of light within the context of seventeenth-century science and, in particular, its reception by Newton. This emphasis on the Principles is not to deny the historical importance of La Dioptrique, but simply to put it into its proper perspective. The derivation of the sine law of refraction, the discussion of refracting surfaces and the Cartesian ovals, the analysis of vision, and the explanation of the rainbow in the accompany-

4 For a description of the manuscript De grauitutione, see note 70. s On a3 December 1630 Descartes wrote to Mersenne that he was then at work on his theory

of light, which is one of the most important and difficult subjects which I could undertake, i;EFoalmost all of physics is included in it (AT, I, 194). See also AT, I, 179; II, zag, 364-5;

6La Dioptrique, chapter I, AT, VI, 83; Discourse on Method, Optics, Geometry, and Meteorology, Paul J. Olscamp (trans.) (Indianapolis : Bobbs-Merrill, I 965)) 66.


ing Les M&bores are all landmarks in the history of seventeenth-century optics.

In his Principles, Descartes presents his theory of light almost exclusively, and most comprehensively, in the context of the light of the sun and stars. In the terrestrial part of the Principles, he treats light only briefly and bases his few explanations on the celestial case. On this account I call Descartes theory of light his celestial optics.

I

Descartes celestial optics

Descartes goal in the third part of his Principles is to construct the entire visible universe and to explain the principal celestial phenomena, of which light is one of the most important. He attempts to derive all the celestial phenomena in accordance with the principles of matter and motion which he had laid down in the preceding part of the Principles, and from the single assumption that the heavens are fluid. Before we follow Descartes in his construction, I will briefly set forth those principles which are relevant for our purposes.

By reducing all the attributes of matter, such as weight, hardness, and colour, to extension, Descartes in effect identified matter and extension. From this identification it followed that matter is homogeneous, incompressible, fills all space, and allows no void. It also follows that, since there is no void, all motions must be in a circle or ring. For if one body moves, then another must simultaneously occupy the space it left, and a third must occupy the space left by the second, and so on in succes- sion, forming a closed ring of motion. This concept, called antiperistasis, is the foundation of Descartes construction of the vortices.

God, Descartes holds, is the original cause of all the motion in the world, and since He is immutable, He always preserves the same quantity of motion in the universe. All motion obeys three laws of nature, guaranteed by His im- mutability. The first two laws together are a statement of the law of inertia :

The first of these is that every thing insofar as it is simple and undivided, always remains in the same state, as much as it can, and never changes except by external causes.

The next law of nature is that every part of matter, considered separately, never tends to continue to move along deflected [curved] lines, but only along straight lines . . .*

Principles, II, 37, AT, VIII, i, 62; IX, ii, 84, * Ibid., II, 39, AT, VIII, i, 63; IX, ii, 85.


Descartes asserts that the second law is true notwithstanding that many of the particles in the plenum will be deflected from their straight paths by collisions with others, and that in any motion an entire circular ring of motion is instantaneously generated. All motion tends in a straight line because God, who conserves all motion,

. . . conserves it precisely as it is only at that moment of time in which he conserves it, taking no account of it a little before. And although no motion occurs in an instant, it is nevertheless clear that every thing which moves, in each instant that can be designated when it moves, is determined to continue in some direction along a straight line, but never along any curved line.g

Descartes illustrates this with a stone whirled around in a sling with a circular motion. At any instant the stone tends along the tangent, as can be seen when the stone is allowed to leave the sling. Now, however, Descartes introduces an entirely new concept, the centrifugal endeavour away from the centre:

From which it follows that every body which moves circularly continually tends to recede from the centre of the circle which it describes, as we feel in the stone itself with our hand when we swing it around with the sling. And because we will frequently use this consideration in that which follows [and it is of such importance] it will have to be noted carefully and will be considered more fully below.

Descartes has in effect introduced a corollary here, and it is this corollary to the second law, rather than the law itself, that he will develop for his theory of light.

The nature of a fluid is that its parts yield their places easily, offering no resistance to an external force, while the parts of a solid yield only to a force large enough to separate them from one another. From Descartes (erroneous) principle that bodies in motion yield their places without any external force, while bodies at rest require an external force to be moved from their places, it follows that those bodies are fluid which are divided into many small particles which are agitated by diverse motions which are independent of one another; and those bodies are hard [duru] all of whose particles mutually rest beside one another. 1 With this brief review of Descartes principles we are now prepared to follow his construction of the heavens and derivation of the principal celestial phenomena, in particular, light.

9 Principles, II, 39, AT, VIII, i, 63-4; IX, ii, 86. lo Ibid., AT, VIII, i, 64-5; IX, ii, 86. l1 Ibid., II, 54, AT, VIII, i, 71; IX, ii, 94.


In the beginning God divided all the matter in the world into parts of uniform size, a mean between the sizes of all those parts which now compose the heavens. He distributed equally amongst these parts two motions, one a rotation about their own centres, and the other a rotation about a series of external centres. By giving them a motion about their own centres He created a fluid. By the other motion initially bestowed upon them, He formed a series of rotating fluids, called vortices, each having at its centre a fixed star, amongst which the sun is to be included. By the force of this rotation some of the parts gradually became round. The spaces between the round parts, since there is no void, were filled by the scrapings or filings which result from the rounding process.

In accordance with this theory of the creation Descartes classifies the matter in the world into three principal elements. The scrapings, which form the sun and fixed stars, are the first element. The first element moves with such a large velocity that on colliding with larger bodies, it crumbles into small parts which exactly fill the gaps between the larger bodies. The rounded balls, which are larger than the first element but smaller than the bodies we see on the earth, compose the heavens and are the second element. The third element, large and slow compared with the second element, forms the earth, planets and comets. Since the sun and fixed stars emit light from themselves, Descartes explains, the heavens transmit it, and the earth, planets, and comets remit [and reflect] it, we may very well refer this threefold difference in the sense of vision [to be luminous, to be transparent, and to be opaque or dark] to [distinguish] the three elements [of this visible world].

The sun and fixed stars, which occupy the centres of the vortices, are very subtle and very liquid bodies formed from the rapidly moving first element, which flowed to the centre of the vortices, because

after all the parts of the second element were greatly worn down and [rounded], they occupied less space than previously and no longer extended up to the centres, but receding from them equally on all sides, they left round spaces there which were [immediately] filled by the matter of the first element flowing there from all the surrounding spaces.13

To explain the endeavour of the balls of the second element to recede from their centres of rotation, Descartes returns, as he had promised, to the corollary to the second law, the importance of which now becomes clear :

l*Ibid., III, 52, AT, VIII, i, 151; IX, ii, IS+ I3 Ibid., III, 54, AT, VIII, i, 107-8; IX, ii, 130.


It is a law of nature that all bodies which move circularly recede from the centre of their motion, as much as is possible [quantum in se est]. And I will explain as accurately as I can that force by which the little balls of the second element, as well as the matter of the first element gathered around the centres . . . [around which they turn], endeavour to recede from those centres [recedere conantur ab istis centris]. For it will be shown below that light consists in that alone; and many other things depend on the understanding of this.r4

Descartes emphasizes that when he says that the balls endeavour [or even that they have an inclination] to recede from the centres [recedere conari a centris], he is not attributing any process of thought to them. He only means that they are so situated and urged to move that they would indeed move from there, if they were not impeded by any other cause.15

Descartes variously describes light as an endeavour (conatus), tendency, effort, inclination or propension to motion, an action, and a pressure or pressing. l6 One can completely sympathize with Jean-Baptiste Morin, who wrote to Descartes that he found other theories of light easier to refute than his, because with your mind regularly turned to the most subtle and highest speculations of mathematics, you enclose and barricade yourself in your terms and mode of expression in such a way that it seemed, at first, that you would be impenetrable. Underlying this surfeit of terms, however, there is a unity of thought arising from Descartes views on circular motion. Descartes himself repeatedly calls attention to the importance of understanding his views on circular motion, particularly the corollary to the second law, that all bodies endeavour to recede from the centre about which they rotate. The key to understanding Descartes theory of light lies in his use of the concept of conatus, which entails that light is an endeavour to motion rather than an actual motion. One motive for introducing this distinction is that if light were an actual motion, then a complete ring of motion would be generated, which would violate the law of rectilinear propagation.

I4 Principles, III, 55, AT, VIII, i, 108; IX, ii, 130-r ; italics added. is Ibid., III, 56, AT, VIII, i, 108; IX, ii, 131. I6 The Latin noun conatus is translated into French as effort or inclination; the verb

conor is translated as faire effort or avoir de linclination (III, 56). The verbs tendo, in Latin, and tendre, in French, are also used as equivalent to conor and faire effort (III, 57). Conatus can be translated into English as effort, endeavour, inclination, or tendency, but since endeavour was the standard seventeenth-century translation, I will use that translation. Descartes uses the term propensio in his letter to Ciermans [23 March 16381; AT, II, 72. Actio or laction is the most common expression used by Descartes. For his use of pressio and pression see note 28.

i Morin to Descartes (22 February 1638), AT, I, 540, i* Newton makes this point in the Principia, Bk. II, Prop. 43, quoted in note 121.


Descartes concept of conatus has recently received considerable attention, but these studies have been concerned solely with Descartes analysis of the motion of a single particle. l9 For Descartes this was only a preliminary to the many-particle or continuum case which arises in his theory of the vortices. Consequently, I will only briefly discuss the single-particle case. Descartes returns to the example of a stone rotating in a sling and subjects it to a more detailed treatment than previously:

Inasmuch as frequently many different causes act together in the same body and impede the effect of one another, we can say, as we consider one or the other of them, that it tends or endeavours to go [tendere, sive ire conari] towards different directions at the same time.20

Thus, if a stone is rotated circularly in a sling, it truly tends along the circle if all the causes of its movement are considered. But if only its motive force is considered, it tends to go along the tangent; for according to the second law, if the stone left the sling it would move along the tangent and not the circle. Although the sling impedes the stone from actually moving along the tangent, it does not impede its endeavour to move there. If we now consider only that part of the force of the stones motion which is impeded by the sling, then we would say that the stone tends . . . or endeavours to recede from the centrey21 radially outwards along a straight line.

It is easy to apply these considerations on the stone and sling to the balls of the second element rotating in their vortices. Each of the little balls makes an effort to recede from the centre of its vortex, but it is restrained by the others which are beyond it, just as the stone is restrained by the sling. But moreover, there is the additional consideration that, the force in these [little balls] is greatly increased because the outer balls are [continually] pressed by the inner balls, and, at the same time, all of them are pressed by the matter of the first element gathered in the centre of each vortex.22

Two points in Descartes analysis of circular motion are essential. First, there is a centrifugal endeavour only where there is resistance or resisted force. In the case of the stone its force to recede is restrained by the tension of the string. There is no motion along the string, and the

I9 See Gabbey, op. cit. note I, 62-5; Herivel, Background, 54-64; and Richard S. Westfall, Force in Newtons Physics: 7% Science of Dynamics in the Seventeenth Century (London: MacDonald,

Ig7I)> 78-81. Principbs, III, 57, AT, VIII, i, 108; IX, ii, 131. Ibid., AT, VIII, i, Iog; IX, ii, 131. Zbid., III, 60, AT, VIII, i, IIS; IX, ii, 133.


two forces are balanced. In the case of the balls of the second element their motion is resisted by those balls lying beyond them. Descartes concept of centrifugal conatus is essentially an equilibrium requirement that the force urging either the stone or one of the little balls to motion be balanced by a resisting force. 23 Second, this endeavour is always directed along straight lines radially outwards from the centre of rotation. It thus appears ideal for explaining the rectilinear propagation of light.

Before we consider Descartes application of this analysis to the properties of light, it is necessary to examine the validity of the statement often made, that for Descartes light is the centrifugal pressure of the celestial matter.24 A typical formulation of this assertion goes: It is this pressure which constitutes their [the stars] light; a pressure which spreads through the medium formed by the second element along straight lines directed from the centre of the circular movement. A number of fundamental points are made here. It is asserted that (i) light is a pressure, (ii) which arises from a circular motion, and (iii) it is emitted radially from the centre of the motion, i.e. the centre of the sun or star. The first assertion will have to be severely modified, for I will show that Descartes concept of centrifugal endeavour is far from a proper concept of hydrostatic pressure and is more akin to a simple rectilinear pressing or pushing. The second and third assertions must also be modified. Regarding the second point, we will see that the sun itself contributes to the generation of light by its outward pressure-a real and not a centrifugal pressure.25 This, though, has important implications for Descartes theory of light and the third point. As Descartes theory now stands, the sun radiates cylindrically rather than spherically, since all its rays proceed perpendicularly from the axis of rotation, and only in the ecliptic do they radiate from the centre of the sun. Moreover, the sun, as Descartes was aware, radiates from its surface, and not from its centre. Descartes devoted considerable attention to the solution of these problems, to which the remainder of this section is largely devoted.

The explanation of why the sun and fixed stars are round is a rather

23 Gabbey, op. cit. note a, 16-31, has observed that Descartes concept of impact is likewise based on a concept of contest or struggle.

a4 For examnle. E. 1. Aiton. The Vortex Theorv of Planetarv Motions. Annals of Science, 13 (rg57), 258-g; Sabra, op. cit. note 2, 54; and Edmund Whittaker, A History of the Theories of Aether and Electricity, I (New York: Harper, rg6o), 9, all refer to the centrifugal tendency as a pressure, and all ignore the suns contribution to the production of light.

*s Admittedly Descartes himself has added to the confusion on this point, for in III, 55 (quoted at note 14) he states that light is due to the centrifugal endeavour alone. I will return to this point at the end of this section.


straightforward application of the centrifugal endeavour of the little

balls of the second element to recede from the centre of the vortex, and is preliminary to Descartes demonstration that the sun radiates in all directions from every point of its surface. In order to explain the centrifugal endeavour of the balls of the second element, Descartes temporarily ignores the contribution of the first element forming the stars and considers the centre of each vortex to be empty (Figure I) :

Since all the little balls which turn about S in the vortex AEI endeavour to recede from S, as it has already been shown, it is sufficiently clear that all those which are in the straight line SA press each other towards A; and that those which are in the straight line SE press each other towards E, and similarly for all the others. Therefore, if there were an insufficient number of them to occupy all of the space between S and the circumference AEI, all the space which they would not fill would be left at S.26

Since the balls are free to rotate independently of each other they leave a round space at S.

To solve the problem of the suns radiation, Descartes, without his usual fanfare, introduces an approach the full implications of which he could not, or did not, see. If its implications are pursued to their logical consequence, as they were by Newton, they lead to a proper definition of pressure. Descartes approach here is of such importance that it is worth quoting in its entirety (Figure I) :

Moreover, it should be noted that not only do all the little balls which are in the straight line SE press each other towards E, but also each one of them is pressed by all the others which are contained within the straight lines drawn from it tangent to the circumference BCD. Thus, for example, the small ball F is pressed by all the others which are within the lines BF and DF, or in the triangular space BDF, but not however by any others. So that if the space F were empty, at one and the same moment of time, all those little balls in the space BFD, but not however any others, would advance as much as they could in order to fill it. For, just as we see that the same force of gravity, which draws a stone falling in the open air in a straight line to the centre of the earth, also carries it off obliquely, when its rectilinear motion is impeded by an inclined plane: similarly, there is no doubt that the same force, with which all the little balls in space BFD attempt to recede from the centre S along straight lines drawn from that centre, is also sufficient to remove them by lines deviating [somewhat] from that centre.

And this example of gravity [gravitatis] will show this clearly. If we consider the lead balls contained in the vessel BFD [Figure aa] and mutually supporting one another, so that, having made an opening F in the bottom of the vessel,

26Prifzci~les, III, 61, AT, VIII, i, 112-13; IX, ii, 133-4.


Figure 1 From Descartes, Principles, III, 62, AT, VIII, i, I 14

Figure 2 From Descartes, Principles, III, 63, AT, VIII, i, I 14


ball I would descend by the force of its own weight [and by that of the others which are above it], at the same instant another two, 2,2 will follow, and these will be followed by three others, 3,30,3, and so on; so that at the same moment of time that the lowest I will begin to move, all the others contained in the triangular space BFD would simultaneously descend, the others being unmoved.

When the lead balls actually descend they hinder each other from descending farther, as in the case of the two balls 2,2 in Figure 2b. But the little balls of the second element are fluid and do not at all interfere with one another, since they are continually in motion and are only in this particular configuration instantaneously. The example of the lead balls further differs from light, since the force of light does not consist in any duration of motion, but only in a pressing [in pressione] or first preparation to motion, even if perhaps motion itself does not follow from that. With no justification other than an appeal to his analogy, Descartes has arbitrarily introduced the restriction that the balls of the second element at F will be pushed only by those balls in the triangular space BFD, but not however by any others. This restriction, though, is not entirely arbitrary, for it is necessary to preserve rectilinear propagation and, hence, to avoid introducing a true pressure at F; I will return to this point in the next section.

Thus far Descartes has succeeded in explaining that light propagates instantaneously along straight lines or rays, which are simply the direction of pressing of the balls of the second element arising from their endeavour to recede from their centres of rotation, and that these rays extend not

Ibid., 111, 62-3, AT, VIII, i, 113-15; IX, ii, I?++-.=,. ax Ibid., in Le Monde (Chapter 13, AT, XI, 95) Descartes added: So that one can conclude

from this nothing else except that the force with which they tend towards E is perhaps like a trembling, and increases and relaxes at different small blows as they change position, which seems to be a property very proper for light. Thus, any vibrations which Descartes may consider to be in light do not arise from the luminous source itself, but are a sort of background noise arising from the aether which transmits the light. Le Monde ou traits de la lami&, completed in 1633, is an early, suppressed version of the Principles.

a Principles, III, 63, AT, VIII, i, I 15; IX, ii, 135-6. It is important to note that while the noun pressio is used in the Latin, it is translated by the verb sont press&s in the French. Descartes failure to use a precise and consistent term for the concept of pressure, reflects his failure to understand the concept itself. The Latin pressio, as far as I can determine, is used only twice by Descartes in his discussion of light (III, 63, IV, 28), and the French pression but once (Descartes to Morin, [12 September 16381, AT, II, 364). Moreover, the two times the noun pressio is used in the Latin, it is translated into the French by an expression using the verb presser. In fact, Descartes indiscriminately interchanges the words to push and to press. In IV, 26 where premo is consistently used in the Latin, it is translated both by presser and pousser, and even once by agir. Hence, I believe that the pressio should be translated simply as a pressing rather than the technical term pressure, for the latter translation implies the understanding of a concept which Descartes lacked.


only from the centre of the sun and fixed stars, but also from all points of their surface. All the other properties of light, he tells us, can be deduced from this.30 Descartes notes, however, that there is a paradox in his theory: the sun and fixed stars, around which the celestial matter rotates, in no way contribute to the generation of light, i.e. there is light without a luminous source. Light has been considered up to this point to be produced only by the centrifugal endeavour of the little balls of the second element,

. . . so that if the body of the sun were nothing other than an empty space, we would nonetheless see its light, not, of course, as strong, but otherwise no differently than at present. [However, this must be understood only for the light which extends from the sun . . . towards the circle of the ecliptic.13i

This apparent paradox has arisen because Descartes has considered radiation only in directions parallel to the ecliptic and has not yet taken into account the contribution of the sun and stars themselves to the production of light. In order to understand how the sun and stars produce light and radiate in all directions, not just parallel to the ecliptic, the motions of the vortices must be considered in greater detail. The vortices thus far have been considered to be independent of one another, but we must now examine their arrangement in space and their mutual interactions.32

All the vortices in the heavens are arranged so that the poles of each vortex touch the ecliptics of the neighbouring vortices. In this way their motions do not impede one another. As a consequence of this arrangement, the matter of the first element, but not that of the second, continually flows out of the vortices at their ecliptics and into them at their poles. Descartes invokes a complex series of motions for the flow of the first element between the vortices. This series of motions fortunately need not concern us, for Descartes solution to the problem of spherical radiation is essentially a simple one: The first element flows to the sun at the centre of the vortex and presses the surrounding balls of the second element equally in all directions. Descartes characteristically explains the equality of the suns pressure in all directions by means of an analogy:

In the same way that we see that a glass bottle becomes round simply by blowing air through an iron tube into its molten matter, since the air does not

3o PrzYzciples, III, 64, AT, VIII, i, I 15; IX, ii, 136. The instantaneous propagation follows from the perfectly hard, incompressible aether; see Sabra, op. cit. note 2, 54-6.

l Principles, III, 64, AT, VIII, i, 5; IX, ii, 136. 32 Ibid., III, 65-76.


tend with a greater force out of the opening of the bottle into its base than into all the other parts into which it is reflected, and it pushes all these parts equally easily; so the matter of the first element, which enters the body of the sun through its poles, must repel1 equally in all directions all the surrounding little balls of the second element; no less those into which it is only obliquely reflected than those into which it strikes directly.33

With one blow Descartes has resolved both his paradox and the problem of spherical radiation.34

Before concluding this section, we should not fail to note that a major transformation has occurred in Descartes theory of light. In accounting for spherical radiation by a simple outward pressure, Descartes has proposed a mode of producing light which is entirely independent of the centrifugal endeavour. He considers both modes of the production of light to occur simultaneously. Nevertheless, one cannot help noting that the most characteristic and unique feature of his theory of light-the centrifugal endeavour-is now superfluous, for all the properties of light can be accounted for by the new explanation of the simple outward pressure. By Ockhams razor, then, the centrifugal endeavour should be eliminated as the cause of light. 35 As we have seen, though, it remains.

It appears that Descartes did not recognize the failure of the centrifugal endeavour to account for spherical radiation until the Principles was well under way. There are no indications in any of his writings prior to the Principles, either in Le Monde or his correspondence, that he recognized this problem or the paradox that the sun itself is not necessary for the production of light. 36 In all his writing s p rior to the Principles, and even up to article III.55 of the Principles itself, he accounts for light by the

33 Ibid., III, 75, AT, VIII, i, 129-31; IX, ii, 144. s4 It remained for Descartes to establish that each point of the surface of the sun radiates

in all directions, even though the sun presses the subtle matter only normal to its surface. This explanation (III, 77-81), while more complex, is basically identical to the one which he had used to explain the radiation arising from the centrifugal endeavour alone (III, 6x-3).

Jacques Rohault, the author of the most influential Cartesian text on natural philosophy, apparently recognized that the centrifugal endeavour had become superfluous and abandoned it. Instead, he adopted the view that light is due to the motion of the parts of a luminous body which push the surrounding medium outwards; Trait6 dephysique, new edition, I (Paris, 1750), chapter 27, sections 15, xg and 23. Hooke, who in some ways followed Descartes theory of light, likewise adopted this solution, but he went one step further and considered light to be an actual motion; Micrographia: Or Some Physiological Descripions of Minute Bodies Made by Magrzifing Glasses (London: 1665; facsimile reprint, New York: Dover, 1961), 54-7.

36 In fact in Le Monde Descartes makes a statement that indicates that he was unaware of the problemof spherical radiation. In the concluding chapter of Le Mona?, chapter 15, Descartes asserts that his explanation of the heavens corresponds to the celestial phenomena as they are actually seen by the inhabitants of the earth: There is no doubt that they would see the body marked S [the sun] entirely full of light, and similar to our Sun, since this body sends rays from all the points of its surface to their eyes (AT, XI, I 05 ; italics added).

D


centrifugal endeavour alone. It seems, therefore, as if Descartes came upon his insight into the failure of his explanation of light too late to alter his system significantly. In any case, I do not think that he would have eliminated the centrifugal endeavour, for the centrifugal endeavour directed outwards in straight lines, and not pressures and fluids, forms the conceptual framework of his theory of light.

II

Conutus and rectilinear propagation

Although Descartes concept of centrifugal conatus implies a proper concept of pressure, he could not fully pursue this implication-as Newton did-for to do so would violate the law of rectilinear propagation for light. On this last point Descartes was as firm as his most severe critic, for he unquestionably considered light to consist of rays extending in straight lines. Descartes would take a number of small steps towards admitting a pressure, but these were concessions he had to make if his theory were to agree with the observed phenomena. Only so far would he go, but no further.

Whenever Descartes was confronted with any theoretical objection to his theory of light which would compromise rectilinear propagation, he in effect simply rejected the argument, declared it irrelevant, and re- affirmed the observed fact that light does travel in straight lines. When, for example, Morin objected to Descartes that with the various motions which Descartes attributes to the aethereal particles (an agitation to form a fluid, and a rotation to explain colours), he could not understand how light could be propagated in straight lines.37 Descartes responded that, The movement, or rather the inclination to move in a straight line, which I attribute to the subtle matter is sufficiently proved by that alone that the rays of Light do extend in a straight line.38 Descartes was, of course, evading the point at issue, which was not whether light is propagated in straight lines, but whether his theory could account for it. Somewhat later, in a letter to Mersenne, Descartes took a similar stand on rectilinear propagation. He noted that although the rays of the sun cannot penetrate an opaque body, since its pores are not sufficiently straight, the aether does still continue to flow within them, but because of that, it does not illuminate their internal parts, since it does not push

37 Morin to Descartes (12 August 1638) AT, II, 293. 3s Descartes to Morin [IZ September 16381, AT, II, 366.


them strongly in a straight line, and it is onb this bushing in a straight line which is called Light.39

As we saw in the preceding section, Descartes recognized that a simple radial endeavour was inadequate to explain the properties of light. To explain how the centrifugal endeavour acting in a unique direction normal to the suns surface could push the surrounding celestial matter in all directions, Descartes proposed the analogy of the lead balls enclosed in a vessel. His problem was to explain how a ball which initially has a tendency to move in one direction alone (the lead balls downwards due to gravity, the balls of the second element radially outwards due to the centrifugal endeavour) also tends to move in other directions. His solution, which he inferred from his analogy, was that the balls rest upon one another and push their neighbours in directions deflected from the vertical. This followed directly from the geometrical properties of spheres in contact subject to an external force. To establish the existence of a tendency to motion in a direction other than the original one, Descartes applied an operational definition of conatus: would the balls move in that direction if they were not resisted or impeded from moving there by the other balls?40 For light ( F ig ure I) he assumed that the balls at F were removed, and for the lead balls (Figure 2) that a small section F at the bottom of the supporting vessel was removed. He then asserted, without any justification other than an appeal to the analogy with the lead balls, that only those balls in the triangular area with vertex at F would tend to move toward F. His operational definition of conatus should lead to a proper concept of pressure, which acts in all directions at any point, but he could not admit this without admitting a violation of rectilinear propagation. Descartes did admit a true pressure at the surface of the sun, but he admitted this because he had to account for the suns radiation in all directions from every point of its surface.

The treatment of this problem in Le Monde is entirely different and far more revealing. Rather than resorting to an analogy, Descartes there attempts to prove the rectilinear propagation of light and to derive the secondary conatus, which deviates from the original direction, directly from physical principles. He tells us that the balls at E (Figure 3) are

39 Descartes to Mersenne [December 16381, AT, II, 468-g; italics added, although Descartes had put Light in italics.

4o Descartes explicitly formulated his operational approach in Le Monde, chapter 13. To determine if a given ball is pressed, it is considered to be removed, since there is no better way to know if g body is pushed by some others than to see if they would actually advance to its place to fill it, when it is empty (AT, XI, 88).


Figure 3 From Descartes, Le Monde, Ch. 13, AT, XI, 87

pressed by all those between lines AE and DE and by the matter of the sun,

. . . which is the cause that they [the balls at E] tend not only towards M, but also towards L, and towards N, and generally towards all the points to which the rays, or straight lines, which pass through their place and come from some part of the sun, can extend.41

41 Le Monde, chapter 13, AT, XI, 88; italics added. I have modified Descartes presentation somewhat to bring it into agreement with that in the Principles. In Le Monde Descartes considers a finite space EFG rather than a point E, as he does in the Principles. My modification changes none of the fundamental principles involved. The phrase in square brackets is my addition.


The balls outside triangular area AED, such as those at H and K, do not tend towards E,

. . . although the inclination that they have to recede from the point S disposes them there in some way [en quelque sorte]. . . .

But the cause which hinders them from tending to this space is that all movements continue, as much as is possible, in a straight line, and consequently when Nature has several ways [aores] to attain the same effect she always infallibly follows the shortest [la plus courte].42

If the balls of the second element at K advanced to E, they would fill E but leave K empty; but at the same time all those nearer the sun would move to fill the gap at K, and there would still be an empty space. The same effect, however, can follow much better, if only those balls which are between lines AE and DE would advance towards E and fill it. Thus those at K will not tend to E, no more than a stone ever tends to descend obliquely towards the centre of the earth, when it can descend there in a straight line.43 (Note that Descartes appeals to an analogy to weight, which acts in a straight line, rather than to pressure, which does not.)

The most important aspect of this argument is Descartes somewhat paradoxical, or even contradictory, position. On the one hand, he admits that there is in some way (en quelque sorte) an internal pressure, or tendency of the aethereal fluid at H and K to move towards E. On the other hand, he denies that the balls at H and K do press towards E. I believe this is the origin of the phrase en quelque sorte. Descartes is directly facing up to-and rejecting-what later became Newtons objection to a continuum theory of light, namely, that a pressure will spread into the geometric shadow after passing through an aperture placed in its path (ZSzci~ia, Bk. II, Prop. 41, Cor.). If the balls at H and K could push those at E, the law of rectilinear propagation would be violated. If we imagine an obstacle placed along EFG with a small hole at E, then the rays from H and K would extend into the unpressed parts beyond rays DEL, AEN. Hence Descartes must necessarily deny that the balls at H and K press those at E. This is a very strange pressure, indeed, which does not act in all directions. This, however, clearly demonstrates Descartes overwhelming commitment to rectilinear propagation--it is only this pushing in a straight line which is called Light.44

Why was this argument omitted from the Principles? I can suggest one

42 Ibid., 89. 43 Ibid., go. 44 See note 39.


important factor which might have contributed to his decision. The principle of shortest path is invalid for optics. It is not at all applicable to refraction, nor even to all cases of reflection, e.g. reflection from a concave, elliptical mirror. Although the inapplicability of this principle was known, Descartes at this time may have been unaware of it, or perhaps only realized the full implications of his argument at a later date. In any case, Descartes application of the principle of shortest path here is rather arbitrary, for he gives no other reason for the balls from H and K not to move to E, than that it is much better if only those balls between lines AF and DE move there. Once he recognized his error, he abandoned the argument, but had no new one to substitute for it.

Descartes, as we have just seen, would have rejected Newtons argument in the corollary to Bk. II, Prop. 41 of the Principia. He also considered-and denied-the proposition itself, that unless the balls of the second element are in a straight line, light is not propagated in a straight line. Once again, Descartes commitment to rectilinear propagation predominates over any other considerations which might compromise that property. In a passage in Le Monde, which was omitted from the Principles, Descartes explains the properties of light; property number four is that light extends ordinarily in straight lines which must be taken for rays of Light:45

4. As to the lines along which this action is communicated and which are properly the rays of light, it is necessary to note that they differ from the parts of the second element through whose medium they are communicated, and that they do not at all consist of the matter of the medium through which they pass, but they designate only the direction and determination along which the luminous body acts. . . . Thus one must not fail to consider them exactly straight, although the parts of the second element which serve to transmit this action, or light, can almost never be so directly placed on one another that they form perfectly straight lines. In the same way you can easily [Figure 4a] conceive that the hand A pushes the body E along the straight line AE, although it pushes it only through the medium of the stick BCD, which is twisted; and in the same way [Figure qb] as the ball I pushes 7 through the medium of the two marked 5,5 as straight as through the medium of the others 2, 3, 4, 6.46

Descartes distinction between the medium which transmits light and the action of light is valid. Yet he cannot so readily eliminate a consideration of the medium from his theory of light, for his theory depends on the balls of the second element more than he recognizes, or at least is willing to

Le Monde, chapter 4, AT, XI, g8. 4-s Ibid., gg-IOO.


a b Figure 4 From Descartes, Le Mode, Ch. 14, AT, XI, loo

admit. In his explanation of the suns radiation in all directions, Descartes introduced the analogy of the lead balls and implicitly and correctly assumed that the balls press one another, thus generating other rays which deviate from the direction of the initial radial conatxs or ray. Descartes, however, could not admit the full implications of this argument-that every ball of the medium, not just those at the surface of the sun, presses all those surrounding it-without violating rectilinear propagation and utterly compromising his theory. Huygens, who was not committed to Descartes theory of light, could admit this implication and, in fact, together with other principles, built his theory of light upon this property. Newton, and before him, Jean-Baptiste Morin, likewise saw this feature of the Cartesian theory, but they launched direct attacks against it.

Morin was the first to criticize this fault in Descartes theory of light. He noted that unless the balls are in a straight line the motion will be interrupted, or will not be rectilinear, but will continue through the contiguous balls.47 Morin recognized that if the balls touch one another,

47 Morin to Descartes (12 August x638), AT, II, 300.

260 Studies in History and Philosofihy of Science

then they will press one another, and light will not be propagated in a straight line. His criticism was well put, and Descartes really evaded the issue when he answered, And for your example of the balls which are not contiguous, I would say to you that it is sufficient that they touch through the medium of some others.48 Descartes did not state why it is sufficient, but instead introduced another example similar to that in L.e Monde (Figure 4b). Morin would not accept Descartes answer, but his response to Descartes remained unanswered, for at this point Descartes broke off the correspondence.49

Morins criticism was perceptive, and he concluded in his unanswered letter that you will be forced to modify the description which you have given of it [light].50 He saw that Descartes theory entailed a violation of rectilinear propagation, since spheres in contact press one another. On this point Newtons criticism, forty years later in the Principia was identical to Morins, and I will return to it below.51

III

Descartes hydrostatics

Descartes, as well as virtually all his contemporaries, had no true understanding of the concept of hydrostatic pressure, although he did allow that a fluid has weight which acts vertically downwards. By not admitting the distinction between the weight and pressure of a fluid, Descartes hydrostatics tended to support his theory of light rather than to contradict it: weight, like light, acts in straight lines. Within two decades after the publication of Descartes Principles, hydrostatics had gone through a revolution, and the concept of pressure-now recognized as distinct from the weight of a fluid-had been properly formulated. From the vantage point of the new hydrostatics, as Newton later so forcefully argued, Descartes theory of light was not tenable. In order to appreciate Newtons reformulation of the foundations of hydrostatics and his criticism of Descartes theory of light, we must first consider Descartes hydrostatics.*

48 Descartes to Morin [IZ September 16381, AT, II, 370. 49 Descartes to Mersenne (15 November 1638), AT, II, 437. Descartes tells Mersenne that

he and Morin have grown further apart as their correspondence has progressed, and therefore he does not wish to continue it.

so Morin to Descartes [October 16381, AT, II, 415. 51 Descartes correspondence with Morin was published in Clerseliers three-volume edition

Lettres de Mr. Descartes (Paris, 1657-67), which Newton had read; see note 75. The following are all extremely useful works on the history of hydrostatics: W. E. Knowles


The prevailing approach to hydrostatics in Descartes day, and even after it, was still based on Archimedes postulate:

It is assumed that a fluid is of such a nature that of the parts of it lying at the same level and adjacent to one another, that part which is pushed less is pushed away by that which is pushed more, and moreover each of its parts is pushed by the fluid which is perpendicularly above it, [if the fluid is sunk in anything and is pressed by anything] .s3

Archimedes admits internal pressures, but they act only vertically, showing that he is actually considering the weight of the fluid rather than its pressure ; while he does posit lateral pressures, these are only in the non-equilibrium case. Archimedes application of his postulate was brilliant and was adequate for explaining the experimental phenomena, but it remained theoretically unsatisfactory in its failure to distinguish weight from pressure.54

Simon Stevins Elements of Hydrostatics was the first significant contribution to hydrostatics since Archimedes. Stevins major achievement was his formulation of the hydrostatic paradox, which states that the pressure on the base of a vessel depends on the area of the base and the distance from the base to the upper surface of the water.56 Perhaps the greatest paradox of Stevins hydrostatic paradox is that his derivation of it was wrong, for he confused the weight and pressure of the water. It was only in the Preamble of the Practice of Hydrostatics, which he appended to the Elements, and which develops some of the practical implications of

Middleton, 7% History ofthe Barometer (Baltimore: Johns Hopkins Press, 1964); Charles Thurot, Recherches historiques sur le principe dArchimede, &rue arc&ologique, new series, x8 (1868) ; 389-406, sg (r86g), 42-9, I I 1-23, 284-39, 345-60; ibid., 20 (1870), 14-33; Clifford Truesdell, Rational Fluid Mechanics, 1687-1765, editors introduction, Lconhardi Euleri opera omnia sub auspiciis Socictatis Scimtiarum .Naturalium Helveticae, series II, vol. 12 (Zurich, rg54), ix-cxxv; Cornelius de Waard, LEx@ience barom&rique: ses ant&dents et ses explications (Thouars: Deux- Sevres, 1936); and Charles Webster, The Discovery of Boyles Law, and the Concept of the Elasticity of Air in the Seventeenth Century, Archive for History of Exact Sciences, 2 (rg65), 441-502.

s3 Archimedes, Opera omnia, II, J. L. Heiberg (ed.) (Leipzig, 1881), 359. The enigmatic phrase in brackets should read: if the fluid is not enclosed in anything and is not compressed by anything else; see E. J. Dijksterhuis, Archimedes, C. Dikshoorn (trans.) (Copenhagen: Munksgaard, rg56), 373. The corrected version of this postulate only became known with Heibergs discovery of the Greek text in x899, and thus only the incomprehensible Latin version was available in the period which concerns us.

s4 See Pierre Duhem, ArchimMe connaissait-il le paradoxe hydrostatique? Bibliotecha Mathematics, series III, I (rgoo), 15-19.

55 De Beghinseln des Waterwichts (Leyden, 1586). Willebrod Snel translated Stevins complete works into Latin in 1605-8, and Albert Girard into French in 1634. The Dutch original with a complete English translation is included in volume I of The Principal Works of Simon Stevin, E. J. Dijksterhuis (ed.) (Amsterdam: Swets & Zeitlinger, 1955).

56 Stevin, Elements of Hydrostatics, Thm. 8, Works, I, 415.


its propositions, that he recognized the true nature of fluid pressure. Stevins grasp of this concept is evident from his solution to a classical problem of the old hydrostatics: to explain how it is possible that a man can swim underwater without being crushed or injured, when he is under such a great weight. Stevin explained that the man is not crushed, because it is not possible for any part of the body to be moved from its natural place by the weight of the water lying on him, since the water exerts the same pressure on all sides. . . .57 Stevins views were far in advance of his contemporaries and were not widely accepted until the second half of the seventeenth century. Descartes was not alone in rejecting the principles of Stevins hydrostatics. S* Benedetti, Mersenne, Galileo, and Hobbes, like Descartes, did not understand the proper concept of pressure. Isaac Beeckman was a notable exception who understood and further developed Stevins concept of pressure. Beeckman, in fact, introduced Descartes to the science of hydrostatics through Stevins work, but, alas, to no avaiL6

Descartes treatment of hydrostatics in the Principles is brief and is limited to a proof of why bodies do not gravitate, or have no weight, in their natural places :

It is also necessary to consider that in all motion there is a circle of bodies which move simultaneously, as it has already been shown above, and that no body can be carried downwards by its own weight, unless another body of equal size and less weight is carried upwards at the same moment of time. And this is the reason that in a vessel, however deep and wide, the lowest drops of water, or of another fluid, are not pressed by the highest; nor are the individual parts of the base pressed except by as many drops as press it perpendicularly.61

In the first sentence, Descartes states the principles of his hydrostatics, and in the second sentence, two fundamental conclusions derived from these principles. To determine if a pressure actually exists, however, Descartes implicitly invokes an additional operational principle; he had earlier formulated this principle for Mersenne: there is nothing which presses [quiplse] except that which can descend when the body on which

Stevin, Elements of Hydrostatics, 4gg-501. * Descartes wrote Mersenne on 16 October 1639 that I do not remember Stevins reason

why one does not feel the weight of the water when one is under it. Implicitly rejecting Stevins explanation, which he had studied twenty years earlier, Descartes then gave his own erroneous demonstration and concluded that instead of feeling that the water presses him downwards from above, he must feel that it lifts him upwards from below, which agrees with experience (AT, IL 587-Q).

de Waard, op. cit. note 52, 71, 92, 93, 13 I. Ibid., chapter 6; Gaston Milhaud, Descartes savant (Paris: Alcan, Ig21), 34-7. 61 Princijles, IV, 26, AT, VIII, i, 215; IX, ii, 213-14.


it presses [il @se] is removed.62 The two conclusions which Descartes derives from these principles are erroneous: the one denies the existence of internal pressures; and the other contradicts the hydrostatic paradox, for example, for a vessel whose sides slope inwards.

We can gain an insight into Descartes hydrostatics from his derivation of the first conclusion, which is also important for understanding Newtons attitude towards Descartes celestial optics and hydrostatics:

For example, [Figure 51, in the vessel ABC, the drop of water I is not pressed by the others 2,3,4 which are above it, because if these were carried downwards, the other drops 5, 6, 7 or similar ones, would have to rise in their place, which impedes their descent, since they are equally heavy.63

Descartes admits that the drops impede one anothers descent, i.e. that there is a conatus, yet he denies that there is an internal pressure. Hence, if pressure were defined as conatus, there would necessarily be an internal pressure. Descartes refused to make this identification of pressure and

Figure 5 From Descartes, Principles, IV, 26, AT, VIII, i, 2 16

Descartes to Mersenne (30 August 1640), AT, III, 165. s Principles, IV, 26, AT, VIII, i, ~15-16; IX, ii, 114. The French translation concludes

somewhat differently: and because the latter [5, 6, 71 are not less heavy, they retain them in balance, by means of which they impede them from pushing one another.


conatus. Newton, however, did. If pressure is defined as conatus, or impeded motion or force, then not only must it be admitted that there are internal pressures in a fluid, but also that the celestial endeavour is a pressure.

Descartes criterion to determine if there is a hydrostatic pressure is identical to that which he used in the case of light to determine if there was a conatus, namely, would the particle (either a drop of water or a ball of the second element) move if all obstacles were removed. Yet, entirely different-almost opposed-results follow in the two cases. Why is this? Descartes invokes different criteria in the two cases to determine if there is a motion. In his hydrostatics, he invokes antiperistasis, whereas in his optics it never enters into consideration, for by removing the balls of the second element there is no longer a plenum.64 But why this difference? This, I believe, reflects Descartes initial commitments to the observed phenomena. If he were to admit antiperistaks in his theory of light, or a true pressure in either his theory of light or his hydrostatics, it would contradict what were for him established phenomena: light propagates rectilinearly, and bodies do not weigh in their own place. Even when confronted with Stevins and, more importantly, Beeckmans ideas on hydrostatic pressure, Descartes did not alter his own hydrostatics.

On one occasion, in La Dioptrique, Descartes did relate his hydrostatics and his optics. The analogy is revealing, both in showing how these two fields were essentially unrelated for Descartes, and in illustrating his use of models and analogies. To illustrate the nature of light ray and its rectilinear propagation through matter, or transparency, Descartes draws an analogy (comparison) to a vat filled with wine and half-pressed grapes (Figure 5). 65 The grapes are analogous to the third element, which forms the solid matter of a transparent body, and the wine to the second element, which fills the pores of all bodies and transmits light. If a very small hole is made in the bottom of the vat, only the wine has a tendency to descend; the grapes rest on one another and therefore have no tendency to descend. If two holes, such as B and 8 (on the right),

64 Under Bee&mans tutelage in late 1618, Descartes attempted to re-derive Stevins formulation of the hydrostatic paradox by use of tbe principle of virtual velocities. While his derivation is beset with other difficulties, Descartes did not here invoke antiperistasis and did not deny the existence of internal pressures. Descartes correctly concluded that Heavy bodies press with equal force all surrounding bodies and, after these have been pushed out [&J&S], would just as easily occupy a lower position (AT, X, 70). Thus, when he did not invoke anti- per&zsis, he arrived at conclusions which directly contradicted his position in the Principles.

65 Lo Diogtrique, chapter I, AT, VI, 86-8; Olscamp, op. cit. note 6, 69-70. I have replaced Descartes figure from La Dioptrique with that of the Principles.

Light, Pressure, and Rectilinear Projagation 2%

are made in the bottom of the vat, the wine at every point of the surface, such as at 7 (on the left), will tend to descend in straight lines through both holes. The upper surface of the wine is analogous to the face of the sun, the openings on the bottom are analogous to our eyes, and the straight lines along which the wine tends to descend are analogous to light rays.

This analysis contradicts Descartes own hydrostatics as he later formulated it in the Principles, where he asserted that no other drops than I, 2, 3, 4, [Figure 51, or others equivalent to them, [the small cylinder of water of which B is the base] press the same part of the base B, because at the same moment of time when this part B can descend, no others [than the cylinder I, 2, 3, 41 can follow it.66 That is, the base is pressed only by the weight of the drops directly above it in a straight line. This conclusion, however, would have been inadequate for his theory of light, since Descartes knew that the suns surface radiates in all directions. He therefore had to switch to an alternative analysis, such as the analogy of the lead balls or the vat of wine. To bring his optics into agreement with the phenomena, Descartes was forced to compromise his hydrostatics by means of these analogies, which, paradoxically, brought his optics closer to a proper formulation of hydrostatics than his hydrostatics itself. These contradictions show that Descartes was not deriving his optics from a theory of fluid mechanics, but rather that he turned to hydrostatics for illustrations or analogies to the phenomena to be explained. This, I believe, explains his somewhat arbitrary use of his models.67 Since Descartes was not really attempting to derive the phenomena from his model, the phenomena to be explained dominated the application of the models. Descartes conceived of his optics in terms of light rays, the force or action of light, and took as his true model of light rays the centrifugal endeavour of the stone whirling in a sling, where the force could actually be felt to be directed radially outwards in a straight line.68 The model of the fluid aether played a subsidiary role to the rays, and Descartes himself insisted that the rays must not be confused with the medium

66 Principles, IV, 26, AT, VIII, i, 216; IX, ii, 214. a For Descartes use of models and analogies, see Gerd Buchdahl, Metaphysics and the Philosofihy

of Science: The Classical Origins: Descartes to Kant (Cambridge, Mass.: MIT Press, rg6g), 133-5, I 40-2. The models of the Diopcs, Buchdahl observes, are in fact on Descartes own admission employed with the utmost abandon and disregard for mutual consistency in their actual physical action, though founded on the basic paradigm of the mechanical laws of matter and motion (ibid., 141-2).

s For the concept of light ray in early seventeenth-century optics, including Descartes, see my Kinematic Optics: A Study of the Wave Theory of Light in the Seventeenth Century, Archivefor History of Exact Sciences, II (Ig73), 134-43.

266 Studies in History and Philosofihy of Science

through which they are propagated. It was only in this way, by thinking in terms of resisted force---conatus or endeavour-that he could appeal to the analogy of the pressing of a twisted stick to support the rectilinear propagation of light (Figure 4a).

Because Descartes had no concept of pressure and considered only the weight of a fluid, which acts in straight lines downwards, he was able to invoke hydrostatics to support his views on the rectilinear propagation of light. Traditional historical accounts have approached Descartes optics from Newtons perspective and have failed to recognize that optics and fluid mechanics were not at all related as they were after Newton. That Newtons view has exerted such a pervasive influence on all later optics and historians of optics, shows how successful he was in redirecting the continuum theories of light and incorporating them into rational fluid mechanics. If one insists on using the terminology of hydrostatics to describe Descartes theory of light, then his concept of light should more properly be described as a weight, and not as a pressure.

IV

Newtons De grabitatione: pressure and conatus

Newtons achievement in hydrostatics lay in providing a theoretical formulation of that science based on pressure rather than on weight. The sciences of hydrostatics and pneumatics had progressed substantially in the twenty years which had intervened between the publication of Descartes Principles and Newtons first encounter with it. The experiments of Torricelli, Pascal and Boyle were all done in this period. Out of their collective endeavours, and those of others, the concepts of the weight, pressure, and elasticity of fluids gradually emerged. The experimental basis for the sciences of pneumatics and hydrostatics, now recognized as one science, was established, but its theoretical foundation was yet to appear. Archimedes postulate, emended somewhat to explain the new experiments, continued to be employed well into the eighteenth century. 6g The only significant attempt to provide hydrostatics with a theoretical foundation was Blaise Pascals Traitez de lequilibre des liquers. Pascals work appeared posthumously in 1663, but there is no evidence that Newton was familiar with it at the time he wrote his De gravitatione

69 Thurot, op. cit. note 52, 20 (1870). 27-8.

Light, Pressure, and Rectilinear Proflagation 267

(c. 1668-70). In any case, their approaches were fundamentally different, for Pascal relied upon the principle of virtual displacements, while Newton always dealt directly with the forces necessary for equilibrium.

Newtons first extant attempt to formulate the principles of hydrostatics, his De gravitatione et aequipondio j%idorum, reflects his deep knowledge-and ultimate rejection-of Descartes Principles of Philosophy. My aim in this section is to analyse Newtons hydrostatics, as he formulated it in the early De gravitatione, and to study its relation to Descartes celestail optics, particularly his concept of conatus.

Newton was thoroughly familiar with the intricate details of Descartes celestial oqtics from the very beginning of his scientific studies. Newtons early notebook, Questiones quaedam philosophicae, in which the scientific entries began in late 1664 and concluded in 1665, is still extant.l A perusal of the contents of the notebook shows that Newton had read Descartes Principles carefully and thoroughly. His attitude towards Descartes theories ranges from outright denial to one of skepticism, as in his opinion Of ye Celestial1 matter & orbes :

Whither Cartes his first element can turne about ye vortex h yet drive ye matter of it continually from ye o to produce light & spend most of it[s] motion in filling up ye chinkes betwix ye Globuli. whither ye least globuli can continue always next ye 0 & yet come always from it to cause light & whither when ye o is obscured ye motion of ye first element must cease (& so whither by his hypothesis ye 0 can be obscured) & whither upon ye ceasing of ye first elements motion ye Vortex must move slower. Whither some of ye first Element comeing . . . immediately from ye poles & other vortexes into

Following the Halls, the manuscript is known by its incijit, De gravitatiane et aequipondia Jluidorum (On the Gravitation and Equilibrium of Fluids). However, the larger incipit, De gravilatione et aequipondio Jluidorum et solidorum in fruidis (On the Gravitation and Equilibrium of Fluids and Solids in Fluids), gives a much better indication of the intended broad scope of the work. The manuscript occupies forty pages of a bound notebook, the remainder of which con- tains blank sheets. It is published with translation in Unpublished Scientijc Pagers of Isaac flewton: A Selection from the Portsmouth Collection in the University Library, Cambridge, A. Rupert Hall and Marie Boas Hall (eds. and trans.) (Cambridge: Cambridge University Press, Ig62), 89-156; henceforth cited as USP. The Halls date the manuscript between 16644, and estimate that it was certainly not later than 1672. Their judgment is based largely on the contents, which show that Newton was still engaged in a detailed study and criticism of Descartes works; USP, 89-90. D. T. Whiteside dates it shortly after 1668, on the basis of the handwriting and from Newtons references to Descartes Let&es, which had been reprinted in a Latin edition in 1668; Before the Princijia: The Maturing of Newtons Thoughts on Dynamical Astronomy, 1664-84, Journal for the History of Astronomy, I (~g~o), 12. Westfall also dates the manuscript from the late 1660s; op. cit. note 19, 403, note 26.

71 A. R. Hall first described and published portions of this notebook; Sir Isaac Newtons Note-Book, 1661-65, Cambridge Historical Journal, g (1g48), 23g-50. W&fall has also described and published portions of it; The Foundations of Newtons Philosophy of Nature, British Journal for the History of Science, I (1g62), 171-82.

268 Studies in History and Philosoghy of Science

all ye parts of or vortex would not impel ye Globuli so as to cause a light from the poles & those places from whence they come.

The details of these points are unimportant, but this passage does show how carefully Newton had read Descartes Principles.

The entry on light is of particular interest, for it already indicates Newtons definite rejection of Descartes theory of light:

Light cannot be by pression &[c] for yn wee should see in ye night a[s] we1 or better yn in ye day. we should se a bright light above us becaus we are pressed downewards . . . ther could be no refraction since ye same matter cannot presse 2 ways. a little body interposed could not hinder us from seing. pression could not render shapes so distinct. ye sun could not be quite eclipsed. ye Moone & planetts would shine like sunns. A man goeing or running would see in ye night. When a fire or candle is extinguish we lookeing another way should see a light . . . a li ht would shine from ye Earth since ye subtill matter tends from ye center. . . . %

Some of the criticism is rather sophomoric--A man goeing or running would see in ye night-while others show a great deal of insight into the system-ye Moone & planetts would shine like sunns. Newton properly infers the latter from the fact that the moon and each planet has its own small vortex rotating about it. From the rotation of the earths own vortex and the consequent outward endeavour of the aether, Newton correctly deduces that a light should arise from the centre of the earth.

Newton is not using the term pression in the sense of an hydrostatic pressure, i.e. a force acting in all directions at any point. He is using it in its then common meaning, as a pressing, just as Descartes had used it; as we will see, in his mechanics from a slightly later period, Newton uses the term pression in a similar sense for the force of impact of colliding bodies. The remark that ye same matter cannot presse 2 ways clearly shows that Newton was still far from understanding the concept of pressure, for he soon recognized that the same matter can-and indeed does--press in all directions. In his mature view Newton would characteristically argue that a pressure would spread completely into the geometric shadow. It is clear, however, that he is here thinking rather of a slight spreading, as is evident from the phrases little body, shapes so distinct, and not be quite eclipsed.

Some four or five years later, at the conclusion of the anni mirubiles, Newton intended to write a treatise, De gravitatione et aequipondio jluidorum, setting forth his newly-wrought science of hydrostatics. Even a casual

72 Wedfall, op. cit., 174. 3 Ibid.; I have altered the punctuation slightly.

Light, Pressure, and Rectilinear Propagation 2%

reading of De gravitatione shows that Newtons hydrostatics was formulated within a Cartesian context, and that he still had Descartes very much in mind. The treatise begins with an introductory paragraph setting forth his methodology and continues with four definitions on space and motion. Newton then interrupted the definitions to begin a note which ultimately filled over three-quarters of the manuscript. This note is a detailed critique of the Cartesian philosophy, which had obviously got somewhat out of hand. Newton himself ultimately realized this and concluded, I have already digressed enough, let us return to the main theme.74 This protracted criticism of Descartes views citing chapter and verse of the Principia philosophiae as well as Clerseliers edition of the Lettres de Mr. Descartes, shows that Newton had a deep and detailed knowledge of the Cartesian system and had not abandoned his concern with it.75 Despite the importance of Newtons criticism I cannot treat it here, for it is beyond my immediate concern and has already received adequate attention.76

The main work on hydrostatics resumes with fifteen more definitions and two propositions before ending abruptly and remaining incomplete. The definitions can be classified into three groups: definitions five to ten deal with forces; definitions eleven to fifteen provide quantitative measures of these forces; and definitions sixteen to nineteen consider properties of matter such as fluidity and elasticity. In the first set of definitions we can see Newton attempting to extend Descartes conatus into a more comprehensive concept which includes hydrostatic pressure:

Def. 5. Force [vis] is the causal principle of motion and rest. And it is either an external [externum] one that generates or destroys or otherwise changes impressed motion in some body; or it is an internal [internum] principle by which existing motion or rest is conserved in a body, and by which any being endeavours to persevere [perseverare conatur] in its state and opposes resistance.

Def. 6. Endeavour [conatus] is an impeded force [vis impedita], or a force insofar as it is resisted.

Def. 7. Impetus is force insofar as it is impressed on another. DeJ 8. Inertia is the internal force of a body, so that its state is not easily

changed by an external exciting force. Def, g. Pressure Lpressio] is the endeavour [conatus] of contiguous parts to

penetrate into each others dimensions. For if they could penetrate the pressure would cease. And pressure is only between contiguous parts, which in turn

s Newton cites Descartes Principles frequently, e.g. USP, 42-5, and the L&m, USP, I 13. KoyrC, op. cit. note 2, 82-94; Hall and Hall, USP, 76-85; and Westfall, op. cit. note 19,

337-41.

E


press upon others contiguous to them, until the pressure is transmitted to the most remote parts of any body, whether hard, soft, or fluid. And upon this action is based the communication of motion by means of a point or surface of contact.

These definitions are far more interrelated than they might at first seem. Figure 6 schematically represents their relation; I have connected vis impedita and vis, since vis impedita is a species of vis.

Despite, or unaware of, a dimensional incommensurability, Newton intended his definition of pressure to encompass both the pressure exerted in impact and static or hydrostatic pressure, for he has defined pressure simply as the endeavour of contiguous parts to penetrate one another, which is a simple pressing equally applicable to hydrostatics and to impact. The broad scope of his definition reflects the central role of the analysis of the problem of impact in the development of his mechanics. Lacking a proper Newtonian concept of force at this time, Newton relied upon his concept of conatus to unify a range of mechanical phenomena all of which have in common an urging or striving, or an impeded or resisted force: centrifugal force, hydrostatic pressure, and the force of impact arising from inertial forces. Newton was apparently attempting to unify the concept of conatus as he had found it in Descartes Principles, for a source for each of Newtons three principal uses of conatus can be found there. Newtons derivation of the centrifugal endeavour, or conatus recedendi a centro, from Descartes has already been demonstrated. Like-

" USP, 114, 148. Def. 5. Vis est motus et quietis causale principium. Estque vel externum quod in aliquod

corpus impressum motum ejus vel generat vel destruit, vel aliquo saltem modo mutat, vel est internum principium quo motus vel quies corpori indita conservatur, et quodlibet ens in suo statu perseverare conatur & imp&turn reluctatur.

Def. 6. Conatus est vis impedita sive vis quatenus resistitur. Def. 7. Impetus est vis quatenus in aliud imprimitur. Def. 8. Inertia est vis interna corporis ne status ejus externa vi illata facile mutetur. Def. 9. Pressio est partium contiguarum conatus ad ipsarum dimensiones mutuo penetran-

dum. Nam si possent penetrare ccssaret prcssio. Estque partium contiguarum tantum, quae rursus premunt alias sibi contiguas donec pressio in remotissimas cujuslibet corporis duri mollis vel fluidi partes transferatur. Et in hat actione communicatio motus mediante puncto vel superficie contactus fundatur. s In addition to the incommensurability of the dimensions of pressure (force/area) and of

impulse (force * time), the concept of pressure cannot apply to forces at a @iat of contact, for with a point the pressure becomes infinite. Newtons reference to communication of motion at a point of contact is, I think, a reference to the impact of hard bodies. Newton held that his derivation of the collision laws was true only in the case of perfectly hard bodies, which touch at only one point; Newton, The Laws of Motion, Herivel, Background, 294. On dimensional incommensurability, see Westfall, ofi. cit. note rq, 551-S.

See Herivel, Background, 454, 54-5; and Westfall, op. cit. note rp, 551~a.

272 Studies in History and Philosojhy of Science

wise, it can be shown that Newtons application of conatus to the force of impact arising from inertial forces derives from Descartes.

In Newtons Waste Book we can see him struggling about 1665 with an analysis of impact. The concepts of force, Indeavour, and pressure introduced in this context were later incorporated into definitions five to nine of De gravitatione. Newton begins section II.e, in Herivels edition of the Waste Book notes on mechanics, with a statement of the principle of inertia, clearly taken from Descartes. * In his extended analysis of the impact of two bodies moving inertially, i.e. moving with a uniform rectilinear velocity, Newton introduces the concepts of force, which he defines as the power of the cause of a change of motion, and Indeavour, which is the application of this force .sl When two bodies a and 6 moving towards one another collide, they will always hinder each others motion, unlesse they could passe the one through the other by penetrating its dimentions.* Moreover, Newton continues,

. . . the cause which hindereth the progression of a is the power which b hath to persever in its velocity or state, and is usually called the force of the body b, and as the body b useth or applyeth this force to stop the progression of a it is said to Indeavour to hinder the progression of a, which endeavour in body [b] is performed by pressure . .

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