  As hydrostatic equilibrium of gaseous discs is partly governed by the gravity
field, we have estimated the component caused by a vertically homogeneous disc,
with a special attention for the outer regions where self-gravity classically
appears. The accuracy of the integral formula is better than 1%, whatever the
disc thickness, radial extension and radial density profile. At order zero, the
field is even algebraic for thin discs and writes $- 4 \pi G \Sigma(R) f_{edge}
(R)$ at disc surface, thereby correcting Paczynski's formula by a multiplying
factor $f_{edge} \gtrsim 1/2$, which depends on the relative distance to the
edges and the local disc thickness. For very centrally condensed discs however,
this local contribution can be surpassed by action of mass stored in the inner
regions, possibly resulting in $f_{edge} \gg 1$. A criterion setting the limit
between these two regimes is derived. These result are robust in the sense that
the details of vertical stratification are not critical. We briefly discuss how
hydrostatic equilibrium is impacted. In particular, the disc flaring should not
reverse in the self-gravitating region, which contradicts what is usually
obtained from Paczynski's formula. This suggests that i) these outer regions
are probably not fully shadowed by the inner ones (important when illuminated
by a central star), and ii) the flared shape of discs does not firmly prove the
absence or weakness of self-gravity.
