D O C U M E N T 1 4 9 A P R I L 1 9 2 2 1 4 1
What is, in undulatory optics, a wave surface is, in emanative optics, a “surface
with an action integral of constant value.”
His optical inquiries thereby take a mechanical turn:
Instead of integrating over the usual differential equations governing the motion
of an (emanative) point of light in the field of force of a given—inhomogeneous
medium, one integrates over the partial differential equation of 1st order which
determines the “surfaces of constant action” and then looks for their orthogonal tra-
jectories.
He soon realizes that this can be taken over from the emanative point of light to
an arbitrary (conservative) mechan. system.
Thus Hamilton made his mechanical discoveries, which Jacobi then perfected in
the “Jacobi-Hamiltonian” integration method (this later merges with Cauchy’s
methods for the integration of part. diff. eqs. of 1st ord. and is completely absorbed
in the integration method by
Lie.[3]
!!!! On the
side,[4]
he discovered conic refraction from the inquiry into how his
emanative-undulatory analysis should be translated from isotropic media to aniso-
tropic ones. (Here the “quadratic” artificial energy
mv2dt
is substituted by a square
root from a fourth-order polynomial.)

.

To Hamilton’s discoveries—or more accurately, to disparate individual results
that diffuse, are furthermore added:
1.° The development of line geometry [Liniengeometrie], which later took on
colossal proportions, thanks to Kummer, Möbius, Plücker, Klein,
Lie.[5]
2.° Bruhn’s theory of “eikonal” optical
instruments.[6]

.

I see just now that in the Jahresbericht der deutschen Mathematiker-Vereini-
gung, vol. 30 (1921), pag. 69, there is a habilitation presentation by G. Prange
(Halle) about
Hamilton.[7]
Hamilton was a really great fellow. It is a shame and very unfortunate that his
papers haven’t been compiled.– (Maxwell published optical studies as a follow-up
to
Hamilton.)[8]

.

p. of light
light rays
˝
˝
˝
Surface: S
mv2dt
const. = =
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