Lenses and Waves

56 CHAPTER 3
was useful at all; did the scholarly world contribute to the art of telescope
making besides revenue, status, and stimuli for progress?
René Descartes definitely believed art could learn from philosophy, and
that it should. In La Dioptrique he intended to show the benefits of
philosophy. The telescope, he said, was a product of practical wit and skills,
but the explanation of its difficulties could bring it to a higher level of
perfection. 11 Just as the telescope surpassed the natural limitations of vision,
so the scholar could teach the craftsman how to overcome his limitations.
The sine law dictated that lenses should have a conical rather than a spherical
shape, as we have seen in the previous chapter. Descartes had also
considered the way his design could be put to practice. In the tenth and final
discourse of La Dioptrique he described the way his lenses could be made. His
account included an ingenious lathe to grind hyperbolic lenses. It reflected
his efforts, during the late 1620s, to make a hyperbolic lens. Descartes was
never lavish to point out his debt to others – to put it mildly – so he did not
tell his readers that he owed much to his cooperation with the lens maker
Jean Ferrier and the mathematician Claude Mydorge. 12 Allegedly, the
threesome succeeded in grinding a convex hyperbolic lens. “And it turned
out perfectly well …”, Descartes wrote in 1635 to Huygens’ father
Constantijn. 13 It had been made by hand. The next step was to design a lathe.
Towards the end of 1628 Descartes left for Holland. In the fall of 1629, he
and Ferrier exchanged some letters in which an earlier design for a lathe was
mentioned. 14 They discussed a machine Descartes had contrived for making a
cutting blade with a hyperbolic edge. 15 Ferrier proposed several modifications
and improvements that turn up in La Dioptrique. 16
Throughout the seventeenth century, Descartes’ account gave rise to
efforts to make elliptic and hyperbolic lenses. Around 1635, Constantijn
Huygens arranged unsuccessful attempts to grind them. 17 In 1643, Rheita
claimed to have succeeded with tools he described in Novem stellae circum
Iovem. Wren described a device to make a hyperboloid surface in an article
published in Philosophical Transactions in 1669. During the 1670s, Huygens
corresponded with Smethwick over another design. 18 Much in these
suggestions never went beyond the paper stage. To execute them skills and
tools – as well as patience – were needed. To design a lens may have been a
scholarly challenge, actually to make it required craftsmanship. And then it
11
Descartes, Dioptrique, 2-3 (AT6, 82-83).
12
Shea, “Descartes and Ferrier”, 146-148.
13
AT1, 598-600. “Et il reussit parfaitement bien; …” It turned out that it was impossible to make a
concave lens in the same way.
14
AT1, lts 8, 11, 12,13,22,21,27. Shea, “Descartes and Ferrier”. The letters not only reveal Ferrier’s
mastery of the art but also his mathematical knowledge.
15
AT1, 33-35.
16
Descartes, Dioptrique, 141-150 (AT6, 215-224).
17
Ploeg, Constantijn Huygens, 34-38.
18
OC7, 111; 117; 487; 511-513. In 1654 Huygens described a mechanism to draw ellipses on the basis of a
circle, apparently aimed at making elliptic lenses out of spherical ones; OC17, 287-292.