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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 treat- ment 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.
239
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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 at- tempted 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 explan- ation 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.
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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 achieve- ment
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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242 Studies in History and Philosophy of Science
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 ana- lysis 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.
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Light, Pressure, and Rectilinear Propagation 243
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 ex- tension. 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.
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244 Studies in History and Philosophy of Science
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 corol- lary 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 construc- tion 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.
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Light, Pressure, and Rectilinear Propagation 245
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.
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246 Studies in History and Philosophy of Science
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 trans- lation.
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.
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Light, Pressure, and Rectilinear Propagation 247
Descartes concept of conatus has recently received considerable
atten- tion, but these studies have been concerned solely with
Descartes analysis of the motion of a single particle. l9 For
Descartes this was only a prelim- inary 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.
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248 Studies in History and Philosophy of Science
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
proper- ties 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 perpen- dicularly 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.
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Light, Pressure, and Rectilinear Propagation 249
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 centri- fugal 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.
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250 Studies in History and Philosophy of Science
Figure 1 From Descartes, Principles, III, 62, AT, VIII, i, I
14
Figure 2 From Descartes, Principles, III, 63, AT, VIII, i, I
14
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Light, Pressure, and Rectilinear Propagation 25
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
trans- lation implies the understanding of a concept which
Descartes lacked.
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252 Studies in History and Philosophy of Science
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 pro- duction 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.
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Light, Pressure, and Rectilinear Propagation 253
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
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254 Studies in History and Philosophy of Science
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.
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Light, Pressure, and Rectilinear Propagation 255
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).
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256 Studies in History and Philosophy of Science
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.
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Light, Pressure, and Rectilinear Propagation 257
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 conse- quently 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.
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258 Studies in History and Philosophy of Science
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
argu- ment in the corollary to Bk. II, Prop. 41 of the Principia.
He also con- sidered-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.
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Light, Pressure, and Rectilinear Propagation 259
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.
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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 under- standing 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 hydro- statics.*
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
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Light, Pressure, and Rectilinear Propagation 261
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 phen- omena, but it remained
theoretically unsatisfactory in its failure to distinguish weight
from pressure.54
Simon Stevins Elements of Hydrostatics was the first significant
contribu- tion 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.
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262 Studies in History and Philosophy of Science
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.
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Light, Pressure, and Rectilinear Propagation 263
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.
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264 Studies in History and Philosophy of Science
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 dif- ference? 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 hydro- statics.
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 for- mulation 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.
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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
for- mulated 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.
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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.
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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
hydro- statics, 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 for- mulated 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.
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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.
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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
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270 Studies in History and Philosophy of Science
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.
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Light, Pressure, and Rectilinear Propagation 271
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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 . .