Lenses and Waves

1655-1672 - DE ABERRATIONE 97
phenomena, he reduced them to concepts already mathematized. To be
more specific: Huygens reduced these dynamical phenomena to the
kinematic groundwork laid by Galileo.
Yoder has pointed out Huygens’ talent for transferring physics to
geometry. 198 His proficiency in idealizing phenomena enabled him to
mathematize not only the abstract objects of mechanics but also concrete
bobs and cords. Once transformed into a geometrical picture, Huygens
could apply his geometrical skills. Just as in his study of spherical aberration,
the kind of experimentation by which Newton had mathematized colors was
absent from Huygens’ studies of circular motion. He was surely a careful
observer and capable of designing clever experiments as an independent
means to test theoretical conclusions. 199 Yet, the precision he achieved in
measuring the constant of gravitational acceleration was made possible by his
mathematical understanding of the matter. Exploring mathematical
properties of a phenomenon empirically was not the way he approached his
objects of study. On the contrary, he readily dismissed Mersenne’s
experiment as indecisive, aware of the imprecision and bias of observation. 200
He approached his subject first of all theoretically, interpreting concepts
geometrically and analyzing phenomena by means of his mathematical
mastery.
In his dioptrical studies, Huygens had likewise relied on his geometrical
proficiency. His theory of spherical aberration was the outcome of rigorous,
sometimes clever deduction. At the point he could have broken really new
ground – when colors emerged – Huygens halted. The process of
geometrizing new phenomena that had proven to be so fruitful in his study
of motion did not get going in dioptrics. Seemingly, he did not see
possibilities to transform those disturbing colors into a geometrical picture,
despite some promising observations he had made of them. However, we
should bear in mind that motion, as contrasted to colors, had already been
mathematized. In his geometrization of circular motion, Huygens could
build on the groundwork laid by Galileo.
Compared to his study of circular motion, De Aberratione was rather
straightforward geometrical reasoning. In this regard, it comes closer to his
study of consonance that occupied him, on and off, from 1661 onwards. 201
The first problem Huygens attacked was the order of consonance, an issue
that had arisen (anew) with the new theories of music of the sixteenth and
seventeenth centuries. In the theory of consonance Huygens adopted, the
coincidence theory of Mersenne and Galileo, the order of consonants was
not evident. He derived a clever rule that only left one problem. His rule
7 seemed to imply that 4 should be placed between the major third and the
198 Yoder, Unrolling time, 171-173.
199 Yoder, Unrolling time, 31-32.
200 Yoder, Unrolling time, 170-171.
201 Cohen, Quantifying music, 209-230 and Cohen, “Huygens and consonance”, 271-301.