Lenses and Waves

THE 'PROJET' OF 1672 133
analogies, despite the fact that it hardly appears in La Dioptrique. 89 Drawing
on the work of Mahoney, he says that the analogies provided a ‘heuristic
model’ that legitimately compared the action of light with the motion of a
ball. By leaving specific material factors in the motion of the ball aside,
Descartes could single out the ball’s tendency to move rather than its
motion. He then was ready to consider this tendency and distinguish
between “… the power, …, which causes the movement of this ball to
continue …” and “… that which determines it to move in one direction
rather than in another, …” 90 According to Schuster this does not refer to a
distinction between force of motion and direction of motion, but to a
distinction between quantity of force of motion and directional magnitude of
force of motion. The two assumptions of Descartes’ derivation are based on
this distinction: the quantity depended on the medium and the parallel
component of directional magnitude was constant. In La Dioptrique
Descartes labeled the directional magnitude with the term ‘determination’ in
order to analyze the components of the action without implicating the
notion of velocity. 91
With this interpretation of the analogies, Descartes’ analysis is not directly
at odds with the system he expounded in Principia Philosophiae and Le Monde.
There he had made the same distinction between quantity and directional
magnitude. The first law of nature states that the quantity of force of motion
is constant when a body is in uniform rectilinear motion; the third law states
that a force of motion is conserved in a unique direction (tangent to the path
of motion). 92 According to Schuster, the tension between the analogies and
the tendency theory can be resolved when Descartes’ heuristic use of the
analogies is interpreted in the terms of his theory of motion. 93 In the light of
the Galilean conception of motion Huygens and Newton employed (as do
we), Descartes’ claim that he derived the laws of optics from his mechanistic
principles was untenable. Sabra has sufficiently pointed this out. 94 Yet, this
was not so much because his system was incoherent or inconsistent as,
rather, because the interpretation of the underlying principles had changed.
Descartes usually considered motion at an instant of impact and discussed it
in terms of the body’s force to move. In the light of this science of motion,
the mathematical derivation of the sine law can indeed be physically
interpreted in a plausible manner. Yet, through his crude presentation in La
Dioptrique Descartes made little effort to prevent misunderstandings and
misinterpretations.
89
Schuster, “Descartes opticien”, 261-272 Schuster, Descartes, 273; Mahoney, Fermat, 387-393; Sabra,
Theories, 78-89.
90
Descartes, AT6, 94-95.
91
Schuster, “Descartes opticien”, 258-261; Schuster, Descartes, 293
92
Schuster, Descartes, 288.
93
Schuster, “Descartes opticien” 261-265.
94
Sabra, Theories, 112-116.