We compute semiclassically and numerically the weights of ray-splitting orb
its in the density of states of a rectangular and an annular ray-splitting
billiard. The agreement between the semiclassical and the numerical results
is very good, confirming the necessity: of including reflection and transm
ission coefficients of non-Newtonian ray-splitting orbits in semiclassical
expressions for the density of states of ray-splitting systems. [S1063-651X
(99)02206-0].