sentiment. It is difficult to render this word into English with full precision. Descartes' own parenthetical explication -- "idea that is formed in our imagination through the intermediary of our eyes" --is of limited help, since at the time of writing The World he had not yet worked out the details of his metaphysics or theory of mind. But it does place sentiments in the mind and makes them more than merely the sensory data connoted by "sensations". Moreover, in Man the brain has sentiments not only of heat and of the color red (note the judgment involved), but also of pain, tickling, and taste. Hence, the term covers both sensations caused by external objects and feelings originating within the body; in an example soon to follow a soldier who mistakenly thinks himself wounded in battle "senses" [sent] both pain and a strap. The mind's involvement in a sentiment tempts one to translate it by "perception", especially since the French cognate does not appear either in The World or in Man. However, it does occur in the Principles of Philosophy and in the Passions of the Soul. The latter includes sentiment among several different sorts of perception. Perception in a general sense is any thought that does not result from the action or will of the soul, and in a restricted sense is "evident knowledge"; sentiment is "what is received in the soul in the same way as objects of the external senses and is not otherwise known by the soul" (Passions, I, 28; AT.XI.349). Perceptions may arise in the imagination, in which case their objects do not really exist. Sentiments arise in the body by the intermediary of the nervous system and, whether really or only apparently, involve the body's external senses. Since here in The World it is the external senses and their relation to the external world that Descartes is discussing, "sensation" seems the best English equivalent.
 Like all university-educated people of his day, Descartes was as fluent in Latin as he was in his native tongue. Not having to translate Latin discourse to understand it, he might well have been unable later to recall in what language he had heard or read something.
 For the theory of mind underlying this argument, see Rule XII of Rules for the Direction of the Mind and Man (AT.XI.170ff.).
 Galileo used this example of the feather drawn lightly over the skin to make roughly the same point about sensory data; see his Assayer (1624), Chap. 48.
 In Discourse I of the Dioptrics Descartes adds to this list of light sources the eyes of cats and other animals that can see in the dark.
 I have added quotation marks here to reflect Descartes' belief that these Aristotelian terms are merely names signifying nothing real.
 Cf. Aristotle, Physics, III, 2, 202a, where in addition the mover must be in contact with the moved.
 Here Descartes hints for the first time that the measure of force in his world is the product of size and speed. The hint never becomes an explicit statement, however, and "size" is later used ambiguously; see below, n.50 .
 Discourse II, "Of Refraction:" "It is only necessary to note that the power, whatever it be, which causes the movement of this ball to continue is different from that which determines it to move in one direction rather than in another, . . ." (Descartes: Discourse on Method, Optics, Geometry, and Meteorology, trans. P.J. Olscamp, Indianapolis, 1965, p.75). On the distinction, which Descartes discusses in greater detail in Chapters 7 and 13 below, see the analyses of A.I. Sabra, Theories of Light from Descartes to Newton (London, 1967), Chapters I-IV, and M.S. Mahoney, The Mathematical Career of Pierre de Fermat (Princeton, 1973; 2nd ed. 1994), App. II.
 Here Descartes invokes for the first of several times a principle of natural economy for which he provides no justification. He states it most clearly below, p. 46: "When nature has many ways of arriving at the same effect, she most certainly always follows the shortest." Neither the nature of matter nor the conserving action of God, both soon to be introduced as the basic principles of the physical universe, seems to imply that nature always takes the most direct path.
 Descartes develops the mechanism for these sensations in Man; cf. AT.XI.143-144.
 en action de. Action acquires a technical meaning in Chap. VII, where Descartes introduces and explains the laws of motion; cf. below, n. 37. But the phrase as used here seems to mean no more than that the balls are in continuing contact and not, as in the next paragraph, touching one another only in passing, i.e. in contact for an instant and no more.
 eaux fortes. F. Alquié, Descartes. Oeuvres philosophiques (Paris, 1963ff), I, 328, n.3, identifies these "strong waters" as nitric acid, used at the time especially for etching copper plates.
 This removal of any upper limit to the size of a part, combined with the absence of any lower limit (cf. Chap. V on the first element), distinguishes Descartes' theory of matter from other atomist and corpuscularist theories, all of which posited a finite, but imperceptibly small size for the ultimate constituents of matter.
 See Rule XII of Rules for the Direction of the Mind, AT.X.424.
 For examples of such "experiments" from the works of the fourteenth-century philosophers Albert of Saxony, Jean Buridan, and Marsilius of Inghen, see Edward Grant (ed.), Source Book in Medieval Science (Cambridge, MA, 1974), 324-328. For later writers, see Charles B. Schmitt, "Experimental Evidence for and against a Void: The Sixteenth-Century Arguments", Isis 58(1967), 352-66.
 The argument here employs unstated premises to achieve a reductio ad absurdum of the theory that vacua exist but that nature "abhors" them. First, it is argued that machines lift great weights before breaking because for, say, a beam to break would require the creation (at least for an instant) of a vacuum between its ruptured parts. But, if so, how could air contain interstitial vacua and still have any body at all (which its resistance to motion through it shows it does)? Why would it not simply dissipate? Second, it is argued that in pumps the water rises against its natural inclination in order to prevent the formation of a vacuum as the piston is withdrawn. But, if so, then why would the water not fall naturally from the clouds to fill interstitial vacua in the air below?
 This motion of mutual replacement is quite reminiscent of Aristotle's antiperistasis, mentioned in Physics IV, 8, 215a, as one possible mechanism for the continued motion of projectiles. Aristotle uses it, however, not to account for motion in a plenum, but to argue against the existence of a vacuum.
 Descartes here again posits a principle of natural economy for which he offers no independent justification; cf. above, n.10. Its application here contravenes the results of his earlier research in hydrostatics while conforming to arguments to be made later (below, Chap. XIII) about the propagation of light through the second element.
 Here the first element assumes the properties of the mathematical continuum. There are no atoms in Descartes' world, just a fragmented continuous space. Cf. above, n.14.
| In traditional Aristotelian cosmology, the four elements were themselves compounds of the terms, taken two at a time, of two pairs of contrary "principles" or qualities: hot--cold and wet--dry. Fire was hot and dry, air hot and wet, water cold and wet, and earth cold and dry. The compositions were often displayed schematically in the form to the right. Reference to the principles here leads to Descartes' statement of his mechanistic program and emphasizes what a radically different approach that program represents. Rather than serving as explanatory constituents of the elements, the principal qualities must be explained in terms of the nature and behavior of those elements.|
 Hence, differing only by size and speed, all elements are transformable into one another merely by change of size or speed.
 Descartes retains here some vestige of the Aristotelian doctrine of natural place. It is no less justified by his argument so far than is his assumption of three elementary states of matter.
 It would seem to follow from Descartes' principles that mixed bodies exist along the surfaces of all the planets. In restricting his claim to the surface of the earth, he may have been reflecting his uncertainty about the theological acceptability of a plurality of (possibly inhabited) worlds.
 Cf. Edward Grant, "Medieval and Seventeenth-Century Conceptions of an Infinite Void Space beyond the Cosmos," Isis, 60(1969), 39-60.
 It is perhaps worth asking here whether Descartes might be hinting at the distinction between a boundless space and an infinite one. On an ocean-covered, spherical earth the surface water, though finite in area, nonetheless appears endless through the absence of any boundaries.
 Descartes here appeals without further explication to his doctrine of clear and evident ideas.
 See below, p.19 , for some elucidation of this remark. There Descartes insists on at least half of the identification of space and matter, i.e. that the essential property of matter is to take up space. Although the arguments just presented against the void would seem to complete the identification, note that God creates matter in an already existing space of indefinite extent.
 Here cosmogony and cosmology are reduced to the same mechanism.
 But, "[We cannot be sure] . . . that He cannot do what we cannot understand; for it would be temerity to think that our imagination is as extensive as His power." Descartes to Mersenne, 15.IV.30, AT.I.14.
 Descartes set out the "others" in the Principles of Philosophy; see below, n. 39.
 Descartes repeats here in somewhat different terms the critique he made in Rule XII of Rules for the Direction of the Mind.
 Aristotle, Physics, III, 1, 201a.
 Although Descartes here places rest and motion on the same ontological level, it is not until the Principles of Philosophy that he argues the relative nature of motion; cf. Principles, Pt. II, pars. 24 and 25.
 Since Descartes has nowhere given quantitative meaning to "motion," it must remain unclear what is being transferred here and what governs that transfer.
 When finally published in the Principles, the rules of impact derived from the laws of motion indeed were "manifestly contrary" to empirical data, as critics immediately pointed out. Descartes anticipated the criticism in Pt. II, par. 53 by noting how difficult it was to single out the bodies involved in any real exchange of motion. He expanded this defense in a letter to Clerselier in February 1645 (AT.IV.183-188) and added to it another version of his principle of economy: When two bodies, which have in them incompatible modes [of motion], collide, some change must certainly take place in these modes to render them compatible, but . . . this change is always the least possible." True to his word in The World, Descartes steadfastly refused to accept empirical evidence against his laws of motion, and several of his followers took an equally stubborn stance after his death.
 Note the determinative role of mathematics in this argument.
 Cf. above, n.12; Here the phrase en action de seems to preserve its meaning, although action has picked up (p. 23 ) the technical sense of inclination to move." So later, for example, light is an action; Chap. XI sets out the properties of the action by which [men's] eyes can be thus pushed [to see light],"but it establishes no parameters by which it might be measured.
 The rules are contained in pars. 45-52 of Part II of the Principles; for a handy schematic presentation, see E.J. Aiton, The Vortex Theory of Planetary Motions (New York, 1972), 36.
 Sapientia, VIII, 21. The statement was a commonplace of medieval thought and was encountered by every schoolboy in the opening line of Johannes de Sacrobosco's Algorismus vulgaris, the standard arithmetic textbook from the mid-thirteenth to the mid-sixteenth century.
 To compound the vagueness of the measure of "motion," Descartes here seems to suggest a non-linear gradient of motion in the vortex, though he offers no reason for it.
 Here again is the non-linear variation of orbital speed with respect to radial distance.
 Descartes shifts here from explication of the mechanism to illustration of it by analogy with more familiar phenomena.
 Compare this explanation with Descartes' theory of the tides, below, Chap. XII.
 The nature and location of the three comets observed in 1618 became the focal issues in an acrid debate between Galileo and the Jesuit astronomer Orazio Grassi. The debate triggered Galileo's masterful Assayer (1624), in which he defended empirical investigation and the use of mathematics and the telescope at the samxtime that he argued that comets were little more than atmospheric optical illusions. For the central texts of that debate, see S. Drake and C.D. O'Malley (trans.), The Controversy on the Comets of 1618 (Philadelphia, 1960).
 In order: Saturn, Jupiter, Mars, Earth, Venus, Mercury.
 This shift from volume to surface as a measure of a body's magnitude only further confuses the question of the parameters of "motion" or "force."
 The surface varies as the square of the ball's radius, the volume as its cube; hence, the ratio of surface to volume varies as 1/radius and so decreases with increasing radius.
 Here again a principle of natural economy substitutes for a missing mechanism; cf. above, n. 10.
 Foremost among the new astronomers, of course, was Galileo, who first reported the moons of Jupiter in his Starry Messenger (1610). Later that year he observed what he thought were satellites about Saturn; he mentioned them in the dedication of his Floating Bodies (1611) to Cosimo II of Tuscany.
 Descartes here introduces the void as a counterfactual hypothesis. He employs the same device later in explicating his theory of light; cf. below, Chap. XIII.
 Descartes had clearly never been down to any depth himself nor talked to anyone who had. Nonetheless, one would think that his hydrostatical investigations and his knowledge of those of Stevin and Beeckman would have compensated for the absence of direct experience. The replacement principle just invoked here is the obverse of Archimedes' famous principle that a body immersed in a fluid loses as much weight as the weight of the fluid displaced.
 This paragraph in particular shows the necessity of the earth's motion in Descartes' universe.
 Compare this and the following chapter to Discourses I and II of the Dioptrics, for which they supply the real model of light.
 It is important to follow the construction of the diagram here, and hence to modify it. Strictly speaking E is a point, the apex of the visual cone EAD. By taking a neighborhood of points about E, Descartes generates a space, which he also calls E. The light coming to that space is the light contained in all the visual cones having a vertex in the space and a base in the sun, i.e. it is the light contained in the truncated cone FADG, where F and G should lie at the upper corners of the space, as shown in the following figure:
The whole argument seems motivated solely by the need to have a person's eye at E see the whole disk of the sun.
 Here again the counterfactual use of the void introduced above; cf. n. 51.
 The principle of economy again; cf. n.10.
 Compare the "packing" argument to follow with the analogy of the wine vat in Discourse I of the Dioptrics.
 Note the virtue of conceiving of light as a force or tendency to move rather than as a motion.
 Discourse II of the Dioptrics.
 On the relation of the real model of light (an impulse propagated instantaneously through a medium) and the heuristic model used in the Dioptrics (a tennis ball moving through empty space), see M.S. Mahoney, The Mathematical Career of Pierre de Fermat (Princeton, 1973, 2nd ed. 1994), App. II.
 Discourse I.
 Thus Descartes removes perhaps the strongest empirical argument against the Copernican system. If, that is, the earth makes an annual circuit about the sun at a distance sufficient to account for observed planetary phenomena, observations of the fixed stars made from opposite sides of the orbit ought to differ by some amount. No one had been able to ascertain any difference, nor would anyone do so until the nineteenth century. Descartes joined Galileo and other defenders by arguing away the point with reference to the immense distance of the fixed stars.
 Among the startling telescopic discoveries announced by Galileo in his Copernican works of the 1610s was the composition of the Milky Way; magnification revealed it to consist of a huge number of separate stars.
 The novae or "new stars" observed in 1572 and 1604 had much to do with the spread of Copernicanism and of opposition to it.
 Note the sloppiness of Descartes' mathematics here. C and D cannot be common points of tangency unless T coincides with S. The error makes clear how little of Descartes' argument in fact rested on mathematical reasoning.
 In the Assayer (trans. Drake in Drake and O'Malley, Controversy (see n.45), 190), Galileo describes the phenomenon as a "curl" [chioma]; Descartes' term is chevelure, which literally means "head of hair."