Lenses and Waves

180 CHAPTER 5
“In this way, I have searched in every detail the properties of the irregular refraction of
this crystal, to see whether each phenomenon that is derived from our hypothesis
agrees with what is actually observed. This being so, it is not a light proof of the truth
of our suppositions and principles.” 58
In glaring contrast with the acuity with which he thus derived the behavior
of strangely refracted rays from his hypothesis stands the vagueness with
which Huygens dealt with the question why light produces spheroidal waves
in Iceland crystal. When he proposed the idea, he said that he only needed to
assume that the speed of light differed for various directions of the crystal:
“As for the other emanation that must produce the irregular refraction, I wanted to try
what elliptical or, speaking better, spheroidal waves would do; and these I supposed
would spread indifferently both in the ethereal matter diffused throughout the crystal
and in the particles of which it is composed; …It seemed to me that the disposition, or
regular arrangement, of these particles could contribute to forming the spheroidal
waves (nothing more being required for this than that the successive movement of light
should spread a little more quickly in one direction than in the other) and I hardly
doubted that there is in this crystal such an arrangement of equal and similar particles,
due to its shape and its angles of definite and invariable measure.” 59
The crucial assumption that light propagates somewhat faster in one
direction of the crystal is being introduced here rather incidentally, in
parentheses. Huygens only vaguely suggested how this assumption in its turn
could be explained mechanistically: by the disposition of the particles of the
crystal. That was about all Huygens said about it, and it was quite meagre
compared to the work he put in accounting for the finite and uniform speed
of light.
At the end of the chapter, Huygens discussed the composition of the
crystal in some detail. He pictured a pile of balls and explained how it would
produce a body with a specific shape. According to this line of reasoning
Iceland crystal would be composed of spheroidally shaped particles.
“… these little spheroids might very well contribute to forming the spheroids of the
light waves assumed above; both being situated the same, and with their axis parallel.” 60
Except for this suggestion, Huygens said nothing about the mechanistic
explanation of his hypothesis. I figure it is quite difficult indeed to explain
58 Traité, 85. “J’ay recherché ainsi par le menu les proprietez de la refraction irreguliere de ce Cristal, pour
voir si chaque phenomene, que se deduit de nostre hypothese, conviendroit avec ce qui s’observe en effet.
Ce qui estant ainsi, ce n’est pas une legere preuve de la verité de nos suppositions & principes.”
59 Traité, 58. “Quant à l’autre émanation qui devoit produire la refraction irreguliere, je voulus essaier ce
que feroient des ondes Elliptiques, ou pour mieux dire spheroïdes; lesquelles je supposay qu’elles
s’estendoient indifferement, tant dans la matiere étherée repandue dans le cristal, que dans les particules
dont il est composé; … Il me sembloit que la disposition, ou arrangement regulier de ces particles,
pouvoit contribuer à former les ondes spheroïdes, (n’estant requis pour cela si non que le mouvement
successif de la lumiere s’étendit un peu plus viste en un sens qu’en l’autre,) & je ne doutay presque point
qu’il n’y eust dans ce cristal un tel arrangement de particules égales & semblables, à cause de sa figure &
ses angles d’une mesure certaine & invariable.”
60 Traité, 96. “J’ajouteray seulement que ces petits spheroides pourroient bien contribuer à former les
spheroides des ondes de lumiere, cy dessus supposez; les uns & les autres estant situez de mesme, & avec
leur axes paralleles.”