Conclusions. The thin disc stars of our local sample are characterised based on values 0 <= e <= 0.32, 0 <= e' <= 0.09, and z(max) = 0.7 kpc. Disc stars satisfy 0 <= e <= 0.44, 0 <= e' <= 0.18, z(max) = 1.5 kpc. The maximum vertical peculiar velocity for disc stars is found to be w(0) = 115 km s(-1). The assumed potential provides a stellar density of the disc vanishing at z0 = 1:8 kpc. The approximate behaviour in the local disc is that a small decrease in the stiffness is associated with a relative decrease in the limiting velocity, which produces a thinner disc and a loss of stars in the local cylinder, both in a similar proportion to the limiting velocity.