  The cosmological constant $(1/2)\lambda_{1}\phi_{, \mu}\phi ^{, \mu}/\phi
^{2}$ is introduced to the generalized scalar-tensor theory of gravitation with
the coupling function $\omega (\phi)=\eta /(\xi -2)$ and the Machian
cosmological solution satisfying $\phi =O(\rho /\omega)$ is discussed for the
homogeneous and isotropic universe with a perfect fluid (with negative
pressure). We require the closed model and the negative coupling function for
the attractive gravitational force. The constraint $% \omega (\phi)<-3/2$ for
$0\leqq \xi <2$ leads to $\eta >3$. If $\lambda_{1}<0$ and $0\leqq -\eta
/\lambda_{1}<2$, the universe shows the slowly accelerating expansion. The
coupling function diverges to $-\infty $ and the scalar field $\phi $ converges
to $G_{\infty}^{-1}$ when $\xi \to 2$ ($t\to +\infty $). The cosmological
constant decays in proportion to $t^{-2}$. Thus the Machian cosmological model
approaches to the Friedmann universe in general relativity with $\ddot{a}=0$,
$\lambda =0$, and $p=-\rho /3$ as $t\to +\infty $. General relativity is
locally valid enough at present.
