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. = =