Hamilton Unboxed!

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May 14, 2019

Hamilton Unboxed!

Or, the tale of the secret compartment and the wave theory of light.

We're back for another Wenner Collection exclusive unboxing video!  Wait to the end to see the secret compartment.

 

This clever box houses four items: “Theory of Systems of Rays” by William Rowan Hamilton from Transactions of the Royal Irish Academy, followed by three supplements to this article.  These articles discuss Hamilton’s characterisitic function, which is the foundation of Hamiltonian mechanics.

The white card is the first thing that I picked out of the box.  Many items in the collection contain these white bookmarks; they are written by David Wenner and describe the significance of the items in the box, publication information, their connection to other items in the Collection, and sometimes provenance information.  Here is the text from the bookmark in this video:


       "'Hamiltonian mechanics' is a reformulation of Lagrangian mechanics that is more useful in describing the motion of complex systems such as planetary orbits and is also better suited to quantum mechanics.  More technically, the Hamiltonian formulation is the 'Legendre transformation' of the Lagrangian formulation, and was based on Hamilton’s 'characteristic function,' which he developed during his work in optics in the 1820s and early 1830s.

Hamilton’s characteristic function is a set of algebraic equations describing the reflection and refraction of a system of rays off simple geometric surfaces like spheres.  This function integrates mechanics, optics, and mathematics, providing a firm footing for the wave theory of light. It was also the foundation upon which Hamilton built his Hamiltonian mechanics.

Hamilton developed his characteristic function through the four papers housed in this box.

'Theory of Systems of Rays'... was delivered while Hamilton was an undergraduate at Trinity College, Dublin. [Transactions of the Royal Irish Academy 15 No. 6 pp. 69-74, 1828]

'Supplement to an Essay on the Theory of Systems of Rays'... developed Hamilton’s approach to geometrical optics. [Transactions of the Royal Irish Academy 16 No. 1 pp. 3-62, 1831]

'Second Supplement to an Essay on the Theory of Systems of Rays'... continued Hamilton’s development of geometrical optics. [Transactions of the Royal Irish Academy 16 No. 4 pp. 93-126, 1831]

'Third Supplement to an Essay on the Theory of Systems of Rays'... presents Hamilton’s 'Characteristic function.'” [Transactions of the Royal Irish Academy 17 Part I No. 1 pp. 1-144, 1837]

- David Wenner