Lenses and Waves

1690 - TRAITÉ DE LA LUMIÈRE 223
understood. 50 This interest displayed in his theory, combined with an
apparent ignorance of its contents, may have influenced the decision to
publish Traité de la Lumière.
In his preface to Traité de la Lumière, Huygens alluded to another reason.
During the 1680s, Leibniz and Newton had published on anaclastic curves.
Huygens had first heard of Newton’s derivation of anaclastic surfaces from
Fatio de Duillier in June 1687. 51 Fatio, who had visited Huygens at the end of
the preceding year, wrote him about the excitement among the members of
the Royal Society over Newton’s forthcoming Principia. According to Fatio,
Newton’s method for finding anaclastic surfaces accorded with Huygens’, in
that he assumed that each ray travels in the same time from one focus to the
other, although he employed a different principle. 52 Huygens, in a letter of 11
July 1687, responded that he did not see how the same conclusion could be
reached from a different assumption. 53 He did not return to the matter in his
correspondence. When Principia was published, he would discover that
Newton assumed bodies instead of waves to travel in equal times. Leibniz, in
the meantime, had also heard of the Principia (he claimed only to have read
the review in Acta eruditorum at that point) and acted appropriately. For
reasons of priority, he sent three articles to the Acta, including one on
anaclastic surfaces. In chapter 6 of Traité de la Lumière, Huygens presented his
own derivation on the basis of his wave theory. In addition, this chapter
contained his determination of caustics by means of his wave theory. It was
an elaboration of the notes of 1677 discussed in section 5.1.1.
Some hold that Newton’s Principia was the main incentive for Huygens to
publish Traité de la Lumière together with his theory of gravity, Discours de la
Cause de la Pesanteur. After he had read the Principia, Huygens wrote his
brother Constantijn in London that he was impressed and would like to
come to Cambridge only to meet Newton. 54 In the summer of 1689, he went
to England and met Newton at the Royal Society. Huygens spoke about his
theories of light and gravity; Newton is reported to have discussed, out of all
possible subjects, strange refraction. 55 Unfortunately, no records remain but
it is likely that the two men did not fully agree. In Principia, Newton had
asserted that a wave-like motion diverts after passing through an aperture.
This implied that waves could not explain the rectilinearity of rays. 56 In
Discours de la Cause de la Pesanteur – a treatise on gravity published together
with Traité de la Lumière – Huygens retarded that waves do spread around
50
OC9, 164.
51
OC9, 167-171.
52
Newton, Principia, 626-628 (Propositions 97 and 98 of section XIV of book I). I do not precisely know
what and how Fatio knew of Huygens’ ideas.
53
OC9, 190.
54
OC9, 305.
55
Westfall, Never at rest, 488; Shapiro, “Pursuing and eschewing hypotheses”, 223.
56
Newton, Principia, 762-767. For an extensive discussion see: Shapiro, “Light, pressure”, 284-291.