  It is known that the trigonometric Calogero-Sutherland model is obtained by
the trigonometric limit (\tau \to \sqrt{-1} \infty) of the elliptic
Calogero-Moser model, where (1,\tau) is a basic period of the elliptic
function. We show that for all square-integrable eigenstates and eigenvalues of
the Hamiltonian of the Calogero-Sutherland model, if \exp (2\pi \sqrt{-1} \tau
) is small enough then there exist square-integrable eigenstates and
eigenvalues of the Hamiltonian of the elliptic Calogero-Moser model which
converge to the ones of the Calogero-Sutherland model for the 2-particle and
the coupling constant l is positive integer cases and the 3-particle and l=1
case. In other words, we justify the regular perturbation with respect to the
parameter \exp (2\pi \sqrt{-1} \tau). With some assumptions, we show analogous
results for N-particle and l is positive integer cases.
