Lenses and Waves

1677-1679 –WAVES OF LIGHT 161
Amidst these various activities there is no sign of further work on the
issues raised in the ‘Projet’. After the inconclusive end of his investigation of
strange refraction, Huygens seems to have let the matter rest. Then, in the
winter of 1675/6 his ‘melancholie’ reared its head again. Huygens went
home to The Hague the following summer, returning to Paris two years later
in June 1678. But he came back with valuable stuff. He had discovered Van
Leeuwenhoek and his microscopes, adding several innovations as well as a
new topic for his dioptrics. And he had a new insight in the nature of light
and the solution to the puzzle of 1672: how can Iceland crystal refract a
perpendicular ray?
5.1 A new theory of waves
On 15 September 1676, Constantijn Sr. wrote to Oldenburg that ‘his
Archimedes’ had brought a piece of that remarkable Iceland crystal with
him. 5 In the Hague, sometime during the next year, Christiaan returned to
the problem of strange refraction. On 14 October 1677 he wrote to Colbert
that he had recently demonstrated the properties of Iceland crystal “…,
which is not a small wonder of nature, nor easy to fathom”. 6 The solution is
found in Huygens’ notebook, right after an investigation of caustics in which
he first formulated his principle of wave propagation. This principle then
turned out to provide the basis for solving the problem strange refraction
posed for waves.
The study of caustics and the solution of strange refraction together take
up 11 pages of the notebook, which in my view form one continuous whole.
However, in their customary manner, the editors of the Oeuvres Complètes
have split up the contents into five paragraphs of the section ‘La Lumière’ in
OC19. 7 They blended material from different pages into what they
considered coherent issues, to the point of inserting material that dates from
years later. 8 This not just disturbs chronology but even Huygens’ actual line
of thinking. I shall now offer my reconstruction of how his conception of
the propagation of waves developed hand in hand with the study of
5 OC8, 19.
6 OC8, 36-37. “… demontrè … depuis peu celle [les proprietez] du Cristal d’Islande, qui n’est pas une
petite merveille de la nature, ni aisée a aprofondir.”
7 Hug9, 38r-48v; OC19, 416-431. With considerable effort, the original order may be reproduced on the
basis of information given in the editors’ annotations. In order to give an idea of the way the manuscript
material has been mixed up in the Oeuvres Complètes, I will list the way the order in which the illustrations
are given (page number in Hug9, number of the illustration in OC19 - section number in OC19. ‘nu’: an
illustration not used) 38r, 137-3, nu (shortest path); 38v, 148-6 (ovals); 39r, 149-6, nu (ovals); 39v, nu nu
nu (ovals); 40r, nu nu (ovals); 40v, 138-3, 139-3, nu nu (shortest path); 41r, 141-4, 144-5, 140-4, nu
(caustics); 41v, 145-5, nu (caustics); 42r, 146-5, nu (caustics); 42v, 150-6 (caustics, wave propagation); 43r,
142-5, 143-5, nu nu (wave propagation, principle); 43v, calculations; 44r, nu nu (telescope and a
wavefront); 44v, nu nu nu (idea of spheroidal wave?); 45r, nu nu nu (idem); 45v, nu (spheroidal waves,
sketch related to Eureka); 46r, ...; 46v, calculations; 47r, 151-7, 152-7, 156-7 (eureka); 47v, nu nu (waves?);
48r, 154-7, 153-7 (shape of crystal); 48v, 147-5, nu nu (athm refraction, (faulty?) propagation (?) of
spheroidal waves)
8 §4 on OC19, 430-431 is of a much later date than the insertion in the section on the explanation of
August 1677 suggests. With respect to content and place in the notebook it must be closer to the
experiment of August 1679.