Lenses and Waves

192 CHAPTER 5
In Maignan’s and Barrow’s elaborations of the sketchy theory of Tractatus
opticus, this problem only got worse. Both transformed Hobbes’ theory into
an emission theory by interpreting a line of light explicitly as a moving body.
I have discussed Barrow’s explanations of reflection and refraction in section
4.1.3. He did invoke a general law of motion to justify his claim that a rod
‘gyrates’ in the way he claimed, but the status of this law was unclear, to say
the least. As a matter of fact, around 1680 the physical pendulum was the
only rigid body whose motion was understood mathematically. 90 The
difference with Huygens’ wave theory is clear. His waves were not some
coherent body but the effect of motions of ethereal particles. 91 In the guise of
a macroscopic model he advanced empirical evidence for his basic claim –
that this action propagates with finite speed and does not displace the
ethereal particles. Moreover, he knew the laws governing impact. 92 We may
infer that this is what Huygens meant with ‘raisons de mechanique’. The
mechanisms assumed to be at work on the microscopic level ought to be understood on the
macroscopic level. Imperceptible matter should be subject to the laws of an
established science of motion.
Huygens did not mention Hobbes, Barrow, or Maignan, but it is not
difficult to see why he would not accept their theories. They employed the
method of transduction, which extends the properties of macroscopic bodies
to the unobservable motion of corpuscules, in a deficient way. 93 Deficient, to
wit, from the perspective of Traité de la Lumiére. On a qualitative level of
everyday observation they may have thought rigid bodies to behave the way
they claimed, as no laws describing these motion were available,
mathematically the extension was incomplete. By reducing the propagation
of light to the one property of velocity, Huygens steered clear of this pitfall.
He possessed a theory of motion and impact that covered his claims about
the waves propagated in ether, given that ether corpuscles were indeed hard.
In his view he thus had succeeded in applying his beloved rigor of
mathematics to the mechanistic nature of things.
These pitfalls of corpuscular reasoning are accentuated in the theory of
waves Hooke included in his Micrographia (1665). Hooke was one of the
precursors Huygens mentioned in Traité de la Lumière and elsewhere he
severely criticized his theory. From the point of view of the mathematician
Huygens this is to be expected, for exactness was precisely the weakness in
Hooke’s account. Hooke did, however, provide the most detailed and
complete account of colors, experimental and theoretical, of the time, the
very subject Huygens had avoided and would remain silent on. As a
theoretical exposition instead of description of microscopic observations,
90 Shapiro, “Kinematic optics”, 177.
91 Newton also understood that a wave cannot be conceived as some kind of coherent entity without
smuggling in unproven assumptions. Shapiro, “Definition”, 195-196.
92 Although gaps in the transition from the behavior of single particles to waves in the sea of ether may be
pointed out, as Burch has done. Burch, “Huygens’ pulse models”, 56-60.
93 For an exposition of this concept and references to the literature see Shapiro, Fits, 40-48.