A linear m=1 perturbation which varies as
is superposed on
the unperturbed disc described above.
The perturbation is assumed to be isothermal,
because in a Be-star disc the thermal time-scale is
much shorter than the dynamical time-scale.
In the following equations describing the perturbation,
we treat only the lowest-order terms with respect to
the vertical coordinate z.
These assumptions and procedures are the same as those adopted
in Okazaki (1991).
Then, the linearized equations describing
the mass, momentum, and angular momentum conservation are
where 
is the Eulerian perturbation of the density,
and 
the horizontal velocity components
associated with the perturbation,
and 
the surface density given by
[for details of deriving Eqs. (12)--(14), see Okazaki (1991)].
Eliminating 
from Eqs. (12)--(14),
we obtain the following set of equations:
Equations (16) and (17) are
the basic equations for
the linear, one-armed isothermal oscillations in the disc.
Note that Eqs. (16) and (17)
are essentially the same as those used
in Okazaki (1991) and SH,
except that, through 
and 
,
our equations implicitly depend on the effect due to
the radiative force as well as
due to the rotational deformation of the star.
We now consider the boundary conditions to be imposed on
Eqs. (16) and (17).
The eigenmode of interest is the mode confined to
the inner part of the disc.
Since the mode must be evanescent in the outer part,
we adopt
at some large radius 
as the outer boundary condition.
We impose the inner boundary condition at the star/disc interface
.
Since the pressure scale-height of the star near the interface
is much smaller than that of the disc,
the waves in the disc do not penetrate the stellar surface.
Hence, we take
at 
as the inner boundary condition.
