Lenses and Waves

124 CHAPTER 4
Harriot had reconsidered and reapplied traditional methods anew and
found – what might be called – an empirical law of refraction. As contrasted
to Kepler, he had turned to the measurement of refraction, instead of the
theoretical trench-plowing of his hapless correspondent. Harriot does not
seem to have considered the ‘proper cause’ of refraction with which his law
may have been understood. His accomplishments were known only to a
small circle of acquaintances. It is possible that they spread through
correspondence, but he became known as a discoverer of the law of
refraction only in the twentieth century. 66
Around 1620, Willebrord Snel was the next to discover the exact measure
of refraction - again by means readily available to Kepler. He did not publish
his discovery, but it became generally known in the 1660s. How he
discovered the law will remain a matter of conjecture. Snel’s papers on optics
are lost, except for the notes he made in Risner’s Opticae libri quatuor (1606)
and an outline of a treatise on optics discovered in the 1930s. 67 Hentschel has
been the first to make a thorough attempt at reconstruction. In his view, Snel
was inspired by an ‘experimentum elegans’ described by Alhacen and copied
by Witelo that involved a segmented disc lowered into water. This led him to
study the refractaria and, facilitated by his geodetic expertise, to the law of
refraction in secans form. 68 I do not fully agree with Hentschel’s analysis, for
I think that the idea of a contraction of the unrefracted perpendicular ray
may have opened to Snel a more direct route to his discovery. Whichever
interpretation is preferable, the main point is that Snel employed means
readily available to Kepler. What is more, his approach of rational analysis of
mathematical regularities in a set of refracted rays was precisely how Kepler
set about initially. He even analyzed the refractaria from various perspectives,
which makes it all the more surprising that Snel was seemingly unfamiliar
with Paralipomena. 69 It remains to be seen why Snel was successful - or: why
he was satisfied with what he found, as contrasted to Kepler’s fruitless
struggle. Maybe he was less strict in empirical matters or he was - like Harriot
- just lucky with looking at the issue from the right perspective.
Paralipomena and the seventeenth-century reconfiguration of optics
The central concept of perspectiva was the visual ray, which established the
visual relation between objects and observer. 70 In seventeenth-century optics
the concept of ray underwent two substantial changes, both anticipated by
Kepler: the subordination of vision to light and the physicalization of the ray.
66
Lohne, “Geschichte des Brechungsgesetzes”, 160-161. Harriot corresponded with Kepler after the
publication of Paralipomena. The correspondence broke off, however, before Harriot could reveal his
findings. KGW2, 425.
67
The notes are in Vollgraff, Risneri Opticam. The outline was discovered by Cornelis de Waard, who
transcribed and translated it in Waard, “Le manuscript perdu de Snellius”. A German translation is given
in Hentschel, “Das Brechungsgesetz”, 313-319.
68
Hentschel, “Das Brechungsgesetz”, 302-308.
69
Hentschel, “Das Brechungsgesetz”, 334 note 22.
70
Smith, “Saving the appearances”, 86-89.