and 1835. In these papers, Hamilton developed his central principle of "Varying Action". A result of this work is a prediction for transparent biaxial crystals (i.e. monoclinic, orthorhombic or triclinic crystals). A ray of light entering such a crystal at a certain angle would emerge as a hollow cone of rays. This discovery was known as conical refraction. Hamilton found it from the geometry of the wave surface introduced by Augustin-Jean Fresnel, which has singular points. There is a basic mathematical explanation of the phenomenon, namely that the wave surface is not the boundary of a convex body. A fuller understanding awaited the microlocal analysis of the middle of the 20th century, The step from optics to dynamics in the application of the method of "Varying Action" was made in 1827, and communicated to the Royal Society, in whose Philosophical Transactions for 1834 and 1835 there are two papers on the subject. Context and importance of the work Hamiltonian mechanics was a powerful new technique for working with equations of motion. Hamilton's advances enlarged the class of mechanical problems that could be solved. His principle of "Varying Action" was based on the calculus of variations, in the general class of problems included under the principle of least action which had been studied earlier by Pierre Louis Maupertuis, Euler, Joseph Louis Lagrange and others. Hamilton's analysis uncovered deeper mathematical structure than had been previously understood, in particular a symmetry between momentum and position. The credit for discovering what are now called the Lagrangian and Lagrange's equations belongs also to Hamilton. Both the Lagrangian mechanics and Hamiltonian approaches have proven important in the study of continuous classical systems in physics, and quantum mechanical systems: the techniques find use in electromagnetism, quantum mechanics, relativity theory and quantum field theory. In the Dictionary of Irish Biography David Spearman writes: Many scientists, including Liouville, Jacobi, Darboux, Poincaré, Kolmogorov, Prigogine and Arnold, have extended Hamilton's work, in mechanics, differential equations and symplectic geometry. Mathematics Hamilton's mathematical studies seem to have been undertaken and carried to their full development without collaboration, and his writings do not belong to any particular school. He was intended by the university authorities who elected him to the Professorship of Astronomy to spend his time as he best could for the advancement of science, without restrictions. Quaternions Hamilton made his discovery of the algebra of quaternions in 1843. Among much prior related