  We discuss capability of Smooth Particle Hydrodynamics to represent
adequately the dynamics of self-gravitating systems, in particular for what
regards the quality of approximation of force fields in the motion equations.
When cubic spline kernels are used, we find that a good estimate of the
pressure field cannot be obtained in non uniform situations using the commonly
adopted scheme of adapting the kernel sizes to include a fixed number of
neighbours. We find that a fixed number of neighbours gives the best
approximation of just the intensity of the force field, while the determination
of the direction of the force requires a number of neighbours which strongly
depends on the particle position.
