  Machian solutions of which the scalar field exhibits the asymptotic behavior
$\phi =O(\rho /\omega)$ are generally explored for the homogeneous and
isotropic universe in the Brans-Dicke theory. It is shown that the Machian
solution is unique for the closed and the open space. Such a solution is
restricted to one that satisfies the relation $GM/c^{2}a=const$, which is fixed
to $\pi $ in the theory for the closed model. Another type of solution
satisfying $\phi =O(\rho /\omega)$ with the arbitrary coupling constant $%
\omega $ is obtained for the flat space. This solution has the scalar field $%
\phi \propto \rho t^{2}$ and also keeps the relation $GM/c^{2}R=const$ all the
time. This Machian relation and the asymptotic behavior $\phi =O(\rho /\omega)$
is equivalent to each other in the Brans-Dicke theory.
