Yes, but later in 1637 Descartes published "La Dioptrique" where he
presented the same result giving what he considered a proof. He didn't
mention Snell or anyone else. He stated that light travels faster in
water than air, although he didn't actually say it with that words
because he even denied the movement of light. His arguments were confusing
and when Fermat saw them (Mersenne sent a copy to him for comments) he
wrote to him asking for a clarification. It then began an acrimonious
controversy between them. Once Descartes was dead, Clerselier, a disciple,
renewed the dispute in 1658, almost twenty years later. In 1662 Fermat
worked out a proof for what he named Descartes law (or Snell law) (The
correspondence is very explicit, especially the letter from Fermat to
M. de la Chambre, Sunday, January 1st. 1662. There is also a summary on
Fermat's letter to M de *** in 1664. Oeuvres de Fermat publiee/s par Paul
Tannery. Gauthier Villars)
> Q2: Was there any consensus at the time that the speed of light was even
> finite? Was this another brilliant insight of Fermat or had there been
> some previous speculation along these lines? His proof, without calculus,
> is brilliant mathematics but what was the status of physical thought at
> the time?
It was a brilliant insight because he said that there must be a
mathematical demonstration in 1637 and he didn't provide one until 1662,
just 2 years before he died. (It could have happened something similar to
his last theorem). He introduced a minimal principle: nature follows the
shortest path. But this was unacceptable for philosophers because it wasn't
a casual law, and predictions couldn't be made. Clerselier told him that it
was ridiculous to accept that nature could change its mind as light travel
through different mediums. Minimal principle were introduced in physics by
Leibniz and Maupertuis the following century.
In 1744, Maupertuis deduced Snell law by applying his Least Action
Principle, and agreeing with Descartes that light travels faster in water
than air. It is a perfect proof with the wrong hypothesis and nobody paid
attention, except prize Nobel Louis Broglie who found (in 1925) that both
Fermat and Maupertuis coincide in certain conditions.
It is a fascinating story of how a physical law is discovered, proved,
misunderstood and given birth to new concepts.
Most references are naturally in french. There is a worth reading book by
George Lochak "La geometrisation de la physique", Ed. Flammarion 1964,
explaining its importance.
Susana MATAIX
Madrid. Spain.
S.MATAIX@teleline.es