  We derive the `exact' Newtonian limit of general relativity with a positive
cosmological constant $\Lambda$. We point out that in contrast to the case with
$\Lambda = 0 $, the presence of a positive $\Lambda$ in Einsteins's equations
enforces, via the condition $| \Phi | \ll 1$, on the potential $\Phi$, a range
${\cal R}_{max}(\Lambda) \gg r \gg {\cal R}_{min} (\Lambda)$, within which the
Newtonian limit is valid. It also leads to the existence of a maximum mass,
${\cal M}_{max}(\Lambda)$. As a consequence we cannot put the boundary
condition for the solution of the Poisson equation at infinity. A boundary
condition suitably chosen now at a finite range will then get reflected in the
solution of $\Phi$ provided the mass distribution is not spherically symmetric.
