  We consider the interior transmission eigenvalue (ITE) problem, which arises
when scattering by inhomogeneous media is studied. The ITE problem is not
self-adjoint. We show that positive ITEs are observable together with plus or
minus signs that are defined by the direction of motion of the corresponding
eigenvalues of the scattering matrix (when the latter approach {\bf$z=1$)}. We
obtain a Weyl type formula for the counting function of positive ITEs, which
are taken together with ascribed signs.
