Euler: From Sound to Light 153
Bernoulli ’ s analogy shows the power of the example of musical sound as a formative
influence in the emergent wave theory of light, in which his theory was an interesting
attempt at a synthesis of Newton ’ s concept of color-making particles with a Cartesian
vortex-filled medium. Bernoulli ’ s use of the analogy with sound followed other attempts
to apply that analogy, including (as we have seen) Newton ’ s own. Bernoulli may well have
drawn on the earlier work of Dortous de Mairan, whose theory of sound had moved the
other direction, by analogy with Newton ’ s color-making particles, to propose the existence
of air particles that could transmit only one specific tone.^3
Though he rejected Huygens ’ s principle and did not discuss interference effects, Ber-
noulli noted that sound can travel obliquely, compared to the rectilinear propagation of
light. In that sense, he follows Newton in denying any positive evidence of wavelike
behavior of light. But where Newton used the same model for the medium of light as for
sound, Bernoulli considered their media to be fundamentally different. He worked out the
mathematics of the displacements of his fibers, noting especially the comparison between
the longitudinal motion of light along a fiber and the transverse displacements of a vibrat-
ing string (that is, its motion perpendicular to itself). Here again, he makes use of what
he considers a “ far-reaching similarity between the motion of the string of a musical
instrument and that of a fiber. ”^4 These two perpendicular kinds of propagation in continu-
ous bodies will return at several points in later developments; for Bernoulli, their differ-
ences and similarities emerged in the context of musical instruments.
When Euler brought forward his own theory of light, “ the most lucid, comprehensive,
and systematic medium theory ” of his century, he first of all posed it on the analogy with
sound, rather than in the context of the long-standing debates between emission and
medium theories.^5 He first announced his theory in a 1744 lecture to the Berlin Academy,
“ Thoughts on Light and Colors, ” whose opening section announces the analogy on which
he builds:There is such a great connection [ rapport ] between light and sound that the more one studies the
properties of these two objects, the more one discovers resemblances. Light and sound both come
to us in straight lines if nothing impedes their movement, and if there are obstacles, the resemblance
does not cease to hold. For as we often see light by reflection or refraction, these two things are
found also in the perception of sound. In its echoes we hear sound by reflection, in the same way
that when we see images in a mirror, the refraction of light is the passage of rays through transparent
bodies, which always produce some change in the direction of the rays; the same thing is found with
sounds, which often pass through walls and other bodies before reaching our ears, so that the walls
and other similar bodies are in connection with sound the same as transparent bodies are for light.
... So great a resemblance does not allow us to doubt that there is such a harmony between the
causes and the other properties of sound and of light, and thus the theory of sound will not fail to
clarify considerably that of light.^6Apparently, this analogy was so coolly received by its first audience that, when Euler came
to write his extended presentation of his “ New Theory of Light and Color ” (1746), he