The propagation of light can be considered in terms of rays and wavefronts in ordinary physical three-dimensional space. The wavefronts are two-dimensional curved surfaces; the rays are one-dimensional curved lines. Hamilton's analogy amounts to two interpretations of a figure like the one shown here. In the optical interpretation, the green wavefronts are lines of constant phase and the orthogonal red lines are the rays of geometrical optics. In the mechanical interpretation, the green lines denote constant values of action derived by applying Hamilton's principle to mechanical motion and the red lines are the orthogonal object trajectories.