DESCARTES, RENÉ DU PERRON (b. La Haye, Touraine, France, 31 March 1596; d. Stockholm, Sweden, 11 February 1650), natural philosophy, scientific method, mathematics, optics, mechanics, physiology.

    a mystery; in the absence of further evidence, one must rest content with the derivations in the Dioptrique.

Following those derivations, Descartes devotes the remainder of the Dioptrique to an optical analysis of the human eye, moving from the explanation of various distortions of vision to the lenses designed to correct them, or, in the case of the telescope, to increase the power of the normal eye. The laws of reflection and refraction reappear, however, in the third of the Essais of 1637, the Météores. There Descartes presents a mathematical explanation of both the primary and secondary rainbow in terms of the refraction and internal reflection of the sun's rays in a spherical raindrop.20 Quantitatively, he succeeded in deriving the angle at which each rainbow is seen with respect to the angle of the sun's elevation. His attempted explanation of the rainbow's colors, however, rested on a general theory of colors that could at the time only be qualitative. Returning to the model of the tennis ball, Descartes explained color in terms of a rotatory motion of the ball, the speed of rotation varying with the color. Upon refraction, as through a prism, those speeds would be altered, leading to a change in colors.

Mechanics.

Descartes's contribution to mechanics lay less in solutions to particular problems than in the stimulus that the detailed articulation of his mechanistic cosmology provided for men like Huygens.21 Concerned with the universe on a grand scale, he had little but criticism for Galileo's efforts at resolving more mundane questions. In particular, Descartes rejected much of Galileo's work, e.g., the laws of free fall and the law of the pendulum, because Galileo considered the phenomena in a vacuum, a vacuum that Descartes's cosmology excluded from the world. For Descartes, the ideal world corresponded to the real one. Mechanical phenomena took place in a plenum and had to be explained in terms of the direct interaction of the bodies that constituted it, whence the central role of his theory of impact.22

Two of the basic principles underlying that theory have been mentioned above. The first, the law of inertia, followed from Descartes's concept of motion as a state coequal with rest; change of state required a cause (i.e., the action of another moving body) and in the absence of that cause the state remained constant. That motion continued in a straight line followed from the privileged status of the straight line in Descartes's geometrical universe. The second law, the conservation of the “quantity of motion” in any closed interaction, followed from the immutability of God and his creation. Since bodies acted on each other by transmission of their motion, the “quantity of motion” (the product of magnitude and speed) served also as Descartes's measure of force or action and led to a third principle that vitiated Descartes's theory of impact. Since as much action was required for motion as for rest, a smaller body moving however fast could never possess sufficient action to move a larger body at rest. As a result of this principle, to which Descartes adhered in the face of both criticism and experience, only the first of the seven laws of impact (of perfectly elastic bodies meeting in the same straight line) is correct. It concerns the impact of two equal bodies approaching each other at equal speeds and is intuitively obvious.

Descartes's concept of force as motive action blocked successful quantitative treatment of the mechanical problems he attacked. His definition of the center of oscillation as the point at which the forces of the particles of the swinging body are balanced out led to quite meager results, and his attempt to explain centrifugal force as the tendency of a body to maintain its determination remained purely qualitative. In all three areas—impact, oscillation, and centrifugal force—it was left to Huygens to push through to a solution, often by discarding Descartes's staunchly defended principles.

Descartes met with more success in the realm of statics. His Explication des engins par l'aide desquels on peut avec une petite force lever un fardeau fort pesant, written as a letter to Constantin Huygens in 1637, presents an analysis of the five simple machines on the principle that the force required to lift a pounds vertically through b feet will also lift na pounds b/n feet. And a memoir dating from 1618 contains a clear statement of the hydrostatic paradox, later made public by Blaise Pascal.23

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