  Effects of the inter-layer couplings for the orthogonal dimer system
SrCu$_2$(BO$_3$)$_2$ are discussed. The spin-gap $\Delta$ of the
three-dimensional model is independent of the inter-layer couplings when they
are small. Therefore at low temperatures ($T < \Delta$) thermodynamic
properties are described well by the two-dimensional model. On the other hand
at high temperatures the mean-field type scaling ansatz is useful to discuss
the magnetic susceptibility for week inter-layer couplings.
  From fit of the magnetic susceptibility, the estimated coupling constants are
J = 85 K for the nearest-neighbor couplings, $J^{'} = 54$ K for the
next-nearest-neighbor couplings, and $J^{''} = 8$ K for the inter-layer
couplings. These parameters are consistent with the temperature dependence of
the specific heat at low temperatures.
