Lenses and Waves

100 CHAPTER 3
see how the different inclinations affected the generation of colors. He might
even have taken a prism to study the effect of twofold refraction on colors.
He might even have measured the angles of the inclination and – even more
speculative – made some measurements on the colors themselves. He did
not, and left colors aside in De Aberratione. In short, he recognized the
importance of the colors displayed by his lenses, but did not know what to
do about them. Which amounts to saying that he did not know what to do
about them mathematically.
3.3.2 HUYGENS THE SCHOLAR &HUYGENS THE CRAFTSMAN
Which brings us back to what Huygens’ study of spherical aberration was all
about: the improvement of telescopes. From the viewpoint of dioptrics,
nothing was wrong with his theory of spherical aberration. It described the
properties, derived from the principles of dioptrics, of light rays when
refracted by spherical surfaces. From the viewpoint of Huygens’ project
there was, however, a serious problem. He did not develop his theory in
order merely to extend his dioptrical knowledge, but to find an improved
configuration of lenses. Huygens’ theory of spherical aberration could not
take colors into account – let alone explain how to minimize their disturbing
effects. From the viewpoint of dioptrical theory, colors were a further effect
yet to be understood; from the viewpoint of De Aberratione they were a fatal
blow. Without the practical goal of De Aberratione, Huygens probably would
never have run across the disturbing colors that spherical lenses also
produced.
I have amply argued that the orientation of Dioptrica on the telescope
marked off Huygens’ dioptrical studies from those of most other
seventeenth-century scholars. He was one of the very few who tried to
acquire a theoretical understanding of the telescope and, in addition, he
wanted to improve the instrument on this basis. That is not necessarily to say
that this practical orientation is characteristic of Huygens’ science in general.
Although applications of theory to instruments were never far from his
mind, his studies of consonance and circular motion were not guided by an
orientation on instruments as his studies of dioptrics were.
The problem of tuning keyboard instruments was important for Huygens’
musical studies but their main goal was the mathematical theory of
consonance. Having elaborated his 31-tone division, he readily saw the
practical application in the guise of a suitable organ, on which one could
switch easily between keys in mean tone temperament. Likewise, his study of
circular motion was aimed at a physical problem (measuring gravity) and
took the form of a thorough, mathematical analysis of circular motion in
many of its manifestations. It was not a analysis of the clock he had invented
earlier, nor did the question which pendulum would be isochronous guide
it. 209 Still, practical thinking of a kind was inherent in Huygens’ study of
209 Yoder, Unrolling time, 71-73.