For a time-periodic Hamiltonian H(p,q,t) of period T, the area crossing a collection of curves at time 0 spanning two homotopic orbits of common period nT, in a time T, is shown to be the difference between the actions, contour integral pdq-Hdt, of the orbits. Similarly in an autonomous Hamiltonian system of two degrees of freedom the flux of energy surface volume per unit time through a surface spanning two homotopic orbits of the same energy is given by the difference between the actions, contour integral p.dq, of the orbits. Analogous results hold for pairs of orbits which converge together in both directions of time.