According to Hamilton's principle, paths which make the action stationary are classical trajectories, but because they travel in imaginary time, the instanton is located in the classically forbidden region beneath the potentials with an energy in the reaction coordinate given by E I = -∂S e /∂τ = ∂S g /∂τ . Halfway along each trajectory, it bounces against a turning point at which V e/g = E I . The length of imaginary time spent on the product (g) state is τ and on the reactant (e) state is βτ . By using a value of τ such that ∂ S ∂τ = 0, we ensure energy conservation of the two trajectories. The instanton thus forms a continuous orbit of imaginary-time period β made up of two trajectories that join smoothly into each other at the hopping point. This is illustrated in the table-of-contents figure.