  The 2-- to 1--dimensional crossover of the localisation length of electrons
confined to a disordered quantum wire of finite width $L_y$ is studied in a
model of electrons moving in the potential of uncorrelated impurities. An
analytical formula for the localisation length is derived, describing the
dimensional crossover as function of width $L_y$, conductance $g$ and
perpendicular magnetic field $B$ . On the basis of these results, the scaling
analysis of the quantum Hall effect in high Landau levels, and the
delocalisation transition in a quantum Hall wire are reconsidered.
