Lenses and Waves

200 CHAPTER 5
mathematical. 125 It assumed a constant difference between the parallel
components of the colored rays. The law can be seen as a natural extension
to dispersion of Descartes’ derivation of the sine law, identifying the variety
of colors with various sizes of the parallel component. 126
In Opticks this ‘Cartesian’ dispersion law has disappeared. Supposedly,
Newton had realized that his dispersion law implied that color depended
upon velocity. This he could not accept, as the immutability of colors was
the core of his theory. As velocity changes in even the most elementary
mechanisms, it seemed a unlikely candidate for an original and conservable
property of light rays. 127 Therefore, the ‘Cartesian’ dispersion law of the
optical lectures was unacceptable. 128 This left a model for dispersion based on
size or mass, but Newton never articulated a mechanism through which
different refrangibility might be explained this way. What is more, the only
mechanism he elaborated for refraction – based on perpendicular forces
acting upon particles – was at odds with such a model, for acceleration is
independent of mass. In Opticks, Newton put forward an alternative law of
dispersion with dubious empirical evidence and whose mechanistic causes he
had never elaborated – not even in private. 129
The status of ‘raisons de mechanique’
In the seclusion of his private quarters, Newton allowed himself a far greater
liberty of reasoning than in his publications. From the very start, his
experimental inquiries had been accompanied by speculations on the
corpuscular nature of light and colors. Shapiro has analyzed the way in which
Newton employed his vibration model to develop his theory of periodicity of
colors. 130 The derivation of the sine law shows that Newton was on a par
with Huygens as regards the mathematization of mechanistic causes. He
employed the method of transduction with a comparable meticulousness
mathematizing the physics of unobservable particles by founding them upon
the established laws of motion. Unfortunately, Newton’s consideration of
‘raison de mechanique’ turned problematic because it produced discrepancies
that left considerable gaps in his mathematical science of colors. It did not
affect his experimental theory of color, though. Although he did not have an
exact law of dispersion, the experimentally disclosed and secured theory of
different refrangibility stood unshaken.
125 Newton, Optical papers 1, 199 & 335-337.
126 See Shapiro, “Dispersion law”, 99-104 & 126-127; Bechler, “Newton’s search”, 4-5. I discuss this
matter in more detail in my “Once Snel breaks down”.
127 Bechler, “Newton’s search”, 32-33.
128 In 1691, Newton figured out a test for the assumption that color differs with velocity: when a moon of
Jupiter disappears behind the planet the slowest color – red – should be seen last. In February 1692,
Flamsteed reported that such a difference could not be observed. This empirical evidence definitely ruled
out velocity. Shapiro, Fits, 144-146.
129 Newton, Opticks, 128-130. Shapiro, “Dispersion law”, 97-99; 126-127. Shapiro suggests that it might be
based upon a small angle approximation of refracting angles.
130 Shapiro, Fits, 200-201.