  We present an estimate of the third integral of motion for axisymmetric
three-dimensional potentials. This estimate is based on a Staeckel
approximation and is explicitly written as a function of the potential. We
tested this scheme for the Besancon Galactic model and two other disc-halo
models and find that orbits of disc stars have an accurately conserved third
quasi integral.
  The accuracy ranges from of 0.1% to 1% for heights varying from z = 0~kpc to
z= 6 kpc and Galactocentric radii R from 5 to 15kpc.
  We also tested the usefulness of this quasi integral in analytic distribution
functions of disc stellar populations: we show that the distribution function
remains approximately stationary and that it allows to recover the potential
and forces by applying Jeans equations to its moments.
